andatoshiki/toshiki-notebook
1
0
Fork 0
mirror of https://github.com/andatoshiki/toshiki-notebook.git synced 2026-06-06 09:16:45 +00:00
Code Issues Actions Packages Projects Releases Wiki Activity
3796c8db6e
toshiki-notebook/academic/physics/ipho-formulas-jpn/10.html

62 lines
130 KiB
HTML
Raw Blame History

This file contains invisible Unicode characters

This file contains invisible Unicode characters that are indistinguishable to humans but may be processed differently by a computer. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

<!DOCTYPE html>
<html lang="en-US" dir="ltr">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width,initial-scale=1">
<title>Formulas for IPhO 日本語版: Section 10 | Toshiki's Note</title>
<meta name="description" content="Toshiki's web notebook served via Vitepress!">
<link rel="preload stylesheet" href="/assets/style.e951b6c8.css" as="style">
<script type="module" src="/assets/app.11c168a7.js"></script>
<link rel="preload" href="/assets/inter-roman-latin.2ed14f66.woff2" as="font" type="font/woff2" crossorigin="">
<link rel="modulepreload" href="/assets/chunks/framework.b7580407.js">
<link rel="modulepreload" href="/assets/chunks/theme.c3ca1c74.js">
<link rel="modulepreload" href="/assets/chunks/commonjsHelpers.725317a4.js">
<link rel="modulepreload" href="/assets/chunks/PageInfo.vue_vue_type_script_setup_true_lang.250b3e56.js">
<link rel="modulepreload" href="/assets/academic_physics_ipho-formulas-jpn_10.md.ebeb60b1.lean.js">
<link rel="stylesheet" href="https://cdnjs.toshiki.dev/ajax/libs/KaTeX/0.16.0/katex.min.css">
<link rel="stylesheet" href="https://cdnjs.toshiki.dev/ajax/libs/font-awesome/6.3.0/css/all.min.css">
<link rel="icon" href="https://r2.toshiki.dev/cdn/toshiki-notebook-favicon/favicon.ico">
<meta name="author" content="Anda Toshiki">
<meta name="keywords" content="Toshiki, Anda Toshiki, andatoshiki, GitHub, GitHub action, Vitepress, Vite, Notebook, Knowledge base, Programming, Programming Notes, Academic, Personal, Notebook, Productivity, Journal, Note-taking, Markdown, Notepad, Organization, Tutorial">
<meta name="google-site-verification" content="lm7PNJiYSPEx1dMast1Xptc0Vk0cU06o-daZSsIgr2I">
<meta name="HandheldFriendly" content="True">
<meta name="MobileOptimized" content="320">
<meta name="theme-color" content="#3c8772">
<meta property="og:type" content="website">
<meta property="og:locale" content="en-US">
<meta property="og:title" content="Toshiki&#39;s Note">
<meta property="og:description" content="Toshiki&#39;s web notebook served via Vitepress!">
<meta property="og:site" content="https://note.toshiki.dev">
<meta property="og:site_name" content="Toshiki&#39;s Note">
<meta property="og:image" content="https://note.toshiki.dev/og-cover.png">
<script>function siteruntime(){window.setTimeout("siteruntime()",1e3),X=new Date("8/24/2021 10:28:00"),Y=new Date,T=Y.getTime()-X.getTime(),M=24*60*60*1e3,a=T/M,A=Math.floor(a),b=(a-A)*24,B=Math.floor(b),c=(b-B)*60,C=Math.floor((b-B)*60),D=Math.floor((c-C)*60),siteruntime_span.innerHTML="This site has been running for: "+A+" day(s) "+B+" hour(s) "+C+" minute(s) "+D+" second(s)"}siteruntime();</script>
<script async defer data-website-id="" src=""></script>
<script id="check-dark-mode">(()=>{const e=localStorage.getItem("vitepress-theme-appearance")||"auto",a=window.matchMedia("(prefers-color-scheme: dark)").matches;(!e||e==="auto"?a:e==="dark")&&document.documentElement.classList.add("dark")})();</script>
<script id="check-mac-os">document.documentElement.classList.toggle("mac",/Mac|iPhone|iPod|iPad/i.test(navigator.platform));</script>
</head>
<body>
<div id="app"><div class="Layout" data-v-f6284a77><!--[--><!--]--><!--[--><span tabindex="-1" data-v-315fcc9b></span><a href="#VPContent" class="VPSkipLink visually-hidden" data-v-315fcc9b> Skip to content </a><!--]--><!----><header class="VPNav" data-v-f6284a77 data-v-ff202323><div class="VPNavBar has-sidebar" data-v-ff202323 data-v-57f83237><div class="container" data-v-57f83237><div class="title" data-v-57f83237><div class="VPNavBarTitle has-sidebar" data-v-57f83237 data-v-87c32abd><a class="title" href="/" data-v-87c32abd><!--[--><!--]--><!--[--><img class="VPImage logo" src="/logos/logo.png" alt data-v-6ebf9bdf><!--]--><!--[-->Toshiki&#39;s Note<!--]--><!--[--><!--]--></a></div></div><div class="content" data-v-57f83237><div class="curtain" data-v-57f83237></div><div class="content-body" data-v-57f83237><!--[--><!--]--><div class="VPNavBarSearch search" data-v-57f83237><!--[--><!----><div id="docsearch"><button type="button" class="DocSearch DocSearch-Button" aria-label="Search"><span class="DocSearch-Button-Container"><svg class="DocSearch-Search-Icon" width="20" height="20" viewBox="0 0 20 20" aria-label="search icon"><path d="M14.386 14.386l4.0877 4.0877-4.0877-4.0877c-2.9418 2.9419-7.7115 2.9419-10.6533 0-2.9419-2.9418-2.9419-7.7115 0-10.6533 2.9418-2.9419 7.7115-2.9419 10.6533 0 2.9419 2.9418 2.9419 7.7115 0 10.6533z" stroke="currentColor" fill="none" fill-rule="evenodd" stroke-linecap="round" stroke-linejoin="round"></path></svg><span class="DocSearch-Button-Placeholder">Search</span></span><span class="DocSearch-Button-Keys"><kbd class="DocSearch-Button-Key"></kbd><kbd class="DocSearch-Button-Key">K</kbd></span></button></div><!--]--></div><nav aria-labelledby="main-nav-aria-label" class="VPNavBarMenu menu" data-v-57f83237 data-v-183ec936><span id="main-nav-aria-label" class="visually-hidden" data-v-183ec936>Main Navigation</span><!--[--><!--[--><a class="VPLink link VPNavBarMenuLink" href="/development/" tabindex="0" data-v-183ec936 data-v-416f44b0><!--[--><span data-v-416f44b0>Development</span><!--]--></a><!--]--><!--[--><div class="VPFlyout VPNavBarMenuGroup active" data-v-183ec936 data-v-62bba1f9><button type="button" class="button" aria-haspopup="true" aria-expanded="false" data-v-62bba1f9><span class="text" data-v-62bba1f9><!----><span data-v-62bba1f9>Academic</span><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" viewbox="0 0 24 24" class="text-icon" data-v-62bba1f9><path d="M12,16c-0.3,0-0.5-0.1-0.7-0.3l-6-6c-0.4-0.4-0.4-1,0-1.4s1-0.4,1.4,0l5.3,5.3l5.3-5.3c0.4-0.4,1-0.4,1.4,0s0.4,1,0,1.4l-6,6C12.5,15.9,12.3,16,12,16z"></path></svg></span></button><div class="menu" data-v-62bba1f9><div class="VPMenu" data-v-62bba1f9 data-v-17c3596a><div class="items" data-v-17c3596a><!--[--><!--[--><div class="VPMenuGroup" data-v-17c3596a data-v-b9d0e57b><p class="title" data-v-b9d0e57b>K-12</p><!--[--><!--[--><div class="VPMenuLink" data-v-b9d0e57b data-v-ec5470f2><a class="VPLink link" href="/academic/chemistry/index" data-v-ec5470f2><!--[-->Chemistry<!--]--></a></div><!--]--><!--[--><div class="VPMenuLink" data-v-b9d0e57b data-v-ec5470f2><a class="VPLink link" href="/discrete-math/index" data-v-ec5470f2><!--[-->Discrete Math.<!--]--></a></div><!--]--><!--[--><div class="VPMenuLink" data-v-b9d0e57b data-v-ec5470f2><a class="VPLink link" href="/academic/literature/index" data-v-ec5470f2><!--[-->Literature<!--]--></a></div><!--]--><!--[--><div class="VPMenuLink" data-v-b9d0e57b data-v-ec5470f2><a class="VPLink link" href="/academic/cis105/index" data-v-ec5470f2><!--[-->CIS105<!--]--></a></div><!--]--><!--]--></div><!--]--><!--[--><div class="VPMenuGroup" data-v-17c3596a data-v-b9d0e57b><p class="title" data-v-b9d0e57b>Tools</p><!--[--><!--[--><div class="VPMenuLink" data-v-b9d0e57b data-v-ec5470f2><a class="VPLink link active" href="/academic/physics/ipho-formulas-jpn/1" data-v-ec5470f2><!--[-->Formulas for IPhO JPN.<!--]--></a></div><!--]--><!--]--></div><!--]--><!--[--><div class="VPMenuLink" data-v-17c3596a data-v-ec5470f2><span class="VPLink" data-v-ec5470f2><!--[--><!--]--></span></div><!--]--><!--[--><div class="VPMenuLink" data-v-17c3596a data-v-ec5470f2><span class="VPLink" data-v-ec5470f2><!--[--><!--]--></span></div><!--]--><!--[--><div class="VPMenuLink" data-v-17c3596a data-v-ec5470f2><span class="VPLink" data-v-ec5470f2><!--[--><!--]--></span></div><!--]--><!--[--><div class="VPMenuLink" data-v-17c3596a data-v-ec5470f2><span class="VPLink" data-v-ec5470f2><!--[--><!--]--></span></div><!--]--><!--[--><div class="VPMenuLink" data-v-17c3596a data-v-ec5470f2><span class="VPLink" data-v-ec5470f2><!--[--><!--]--></span></div><!--]--><!--[--><div class="VPMenuLink" data-v-17c3596a data-v-ec5470f2><span class="VPLink" data-v-ec5470f2><!--[--><!--]--></span></div><!--]--><!--[--><div class="VPMenuLink" data-v-17c3596a data-v-ec5470f2><span class="VPLink" data-v-ec5470f2><!--[--><!--]--></span></div><!--]--><!--]--></div><!--[--><!--]--></div></div></div><!--]--><!--[--><div class="VPFlyout VPNavBarMenuGroup" data-v-183ec936 data-v-62bba1f9><button type="button" class="button" aria-haspopup="true" aria-expanded="false" data-v-62bba1f9><span class="text" data-v-62bba1f9><!----><span data-v-62bba1f9>Application</span><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" viewbox="0 0 24 24" class="text-icon" data-v-62bba1f9><path d="M12,16c-0.3,0-0.5-0.1-0.7-0.3l-6-6c-0.4-0.4-0.4-1,0-1.4s1-0.4,1.4,0l5.3,5.3l5.3-5.3c0.4-0.4,1-0.4,1.4,0s0.4,1,0,1.4l-6,6C12.5,15.9,12.3,16,12,16z"></path></svg></span></button><div class="menu" data-v-62bba1f9><div class="VPMenu" data-v-62bba1f9 data-v-17c3596a><div class="items" data-v-17c3596a><!--[--><!--[--><div class="VPMenuGroup" data-v-17c3596a data-v-b9d0e57b><p class="title" data-v-b9d0e57b>Personal projects</p><!--[--><!--[--><div class="VPMenuLink" data-v-b9d0e57b data-v-ec5470f2><a class="VPLink link" href="/application/markdown-it-katex/how-to-use" data-v-ec5470f2><!--[-->markdown-it-katex<!--]--></a></div><!--]--><!--[--><div class="VPMenuLink" data-v-b9d0e57b data-v-ec5470f2><a class="VPLink link" href="/application/vitepress-plugin-shiki-twoslash/index" data-v-ec5470f2><!--[-->vitepress-plugin-shiki-twoslash<!--]--></a></div><!--]--><!--]--></div><!--]--><!--]--></div><!--[--><!--]--></div></div></div><!--]--><!--[--><div class="VPFlyout VPNavBarMenuGroup" data-v-183ec936 data-v-62bba1f9><button type="button" class="button" aria-haspopup="true" aria-expanded="false" data-v-62bba1f9><span class="text" data-v-62bba1f9><!----><span data-v-62bba1f9>Save</span><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" viewbox="0 0 24 24" class="text-icon" data-v-62bba1f9><path d="M12,16c-0.3,0-0.5-0.1-0.7-0.3l-6-6c-0.4-0.4-0.4-1,0-1.4s1-0.4,1.4,0l5.3,5.3l5.3-5.3c0.4-0.4,1-0.4,1.4,0s0.4,1,0,1.4l-6,6C12.5,15.9,12.3,16,12,16z"></path></svg></span></button><div class="menu" data-v-62bba1f9><div class="VPMenu" data-v-62bba1f9 data-v-17c3596a><div class="items" data-v-17c3596a><!--[--><!--[--><div class="VPMenuLink" data-v-17c3596a data-v-ec5470f2><a class="VPLink link" href="/save/reading/index" data-v-ec5470f2><!--[-->Reading<!--]--></a></div><!--]--><!--[--><div class="VPMenuLink" data-v-17c3596a data-v-ec5470f2><a class="VPLink link" href="/academic/vocabulary/index" data-v-ec5470f2><!--[-->Vocabulary<!--]--></a></div><!--]--><!--]--></div><!--[--><!--]--></div></div></div><!--]--><!--]--></nav><!----><div class="VPNavBarAppearance appearance" data-v-57f83237 data-v-dc7cad42><button class="VPSwitch VPSwitchAppearance" type="button" role="switch" title="toggle dark mode" aria-checked="false" data-v-dc7cad42 data-v-65b67168 data-v-56eb52d1><span class="check" data-v-56eb52d1><span class="icon" data-v-56eb52d1><!--[--><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" viewbox="0 0 24 24" class="sun" data-v-65b67168><path d="M12,18c-3.3,0-6-2.7-6-6s2.7-6,6-6s6,2.7,6,6S15.3,18,12,18zM12,8c-2.2,0-4,1.8-4,4c0,2.2,1.8,4,4,4c2.2,0,4-1.8,4-4C16,9.8,14.2,8,12,8z"></path><path d="M12,4c-0.6,0-1-0.4-1-1V1c0-0.6,0.4-1,1-1s1,0.4,1,1v2C13,3.6,12.6,4,12,4z"></path><path d="M12,24c-0.6,0-1-0.4-1-1v-2c0-0.6,0.4-1,1-1s1,0.4,1,1v2C13,23.6,12.6,24,12,24z"></path><path d="M5.6,6.6c-0.3,0-0.5-0.1-0.7-0.3L3.5,4.9c-0.4-0.4-0.4-1,0-1.4s1-0.4,1.4,0l1.4,1.4c0.4,0.4,0.4,1,0,1.4C6.2,6.5,5.9,6.6,5.6,6.6z"></path><path d="M19.8,20.8c-0.3,0-0.5-0.1-0.7-0.3l-1.4-1.4c-0.4-0.4-0.4-1,0-1.4s1-0.4,1.4,0l1.4,1.4c0.4,0.4,0.4,1,0,1.4C20.3,20.7,20,20.8,19.8,20.8z"></path><path d="M3,13H1c-0.6,0-1-0.4-1-1s0.4-1,1-1h2c0.6,0,1,0.4,1,1S3.6,13,3,13z"></path><path d="M23,13h-2c-0.6,0-1-0.4-1-1s0.4-1,1-1h2c0.6,0,1,0.4,1,1S23.6,13,23,13z"></path><path d="M4.2,20.8c-0.3,0-0.5-0.1-0.7-0.3c-0.4-0.4-0.4-1,0-1.4l1.4-1.4c0.4-0.4,1-0.4,1.4,0s0.4,1,0,1.4l-1.4,1.4C4.7,20.7,4.5,20.8,4.2,20.8z"></path><path d="M18.4,6.6c-0.3,0-0.5-0.1-0.7-0.3c-0.4-0.4-0.4-1,0-1.4l1.4-1.4c0.4-0.4,1-0.4,1.4,0s0.4,1,0,1.4l-1.4,1.4C18.9,6.5,18.6,6.6,18.4,6.6z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" viewbox="0 0 24 24" class="moon" data-v-65b67168><path d="M12.1,22c-0.3,0-0.6,0-0.9,0c-5.5-0.5-9.5-5.4-9-10.9c0.4-4.8,4.2-8.6,9-9c0.4,0,0.8,0.2,1,0.5c0.2,0.3,0.2,0.8-0.1,1.1c-2,2.7-1.4,6.4,1.3,8.4c2.1,1.6,5,1.6,7.1,0c0.3-0.2,0.7-0.3,1.1-0.1c0.3,0.2,0.5,0.6,0.5,1c-0.2,2.7-1.5,5.1-3.6,6.8C16.6,21.2,14.4,22,12.1,22zM9.3,4.4c-2.9,1-5,3.6-5.2,6.8c-0.4,4.4,2.8,8.3,7.2,8.7c2.1,0.2,4.2-0.4,5.8-1.8c1.1-0.9,1.9-2.1,2.4-3.4c-2.5,0.9-5.3,0.5-7.5-1.1C9.2,11.4,8.1,7.7,9.3,4.4z"></path></svg><!--]--></span></span></button></div><div class="VPSocialLinks VPNavBarSocialLinks social-links" data-v-57f83237 data-v-aaebde08 data-v-8a65be56><!--[--><a class="VPSocialLink no-icon" href="https://github.com/andatoshiki" aria-label="github" target="_blank" rel="noopener" data-v-8a65be56 data-v-1b61e2c7><svg role="img" viewBox="0 0 24 24" xmlns="http://www.w3.org/2000/svg"><title>GitHub</title><path d="M12 .297c-6.63 0-12 5.373-12 12 0 5.303 3.438 9.8 8.205 11.385.6.113.82-.258.82-.577 0-.285-.01-1.04-.015-2.04-3.338.724-4.042-1.61-4.042-1.61C4.422 18.07 3.633 17.7 3.633 17.7c-1.087-.744.084-.729.084-.729 1.205.084 1.838 1.236 1.838 1.236 1.07 1.835 2.809 1.305 3.495.998.108-.776.417-1.305.76-1.605-2.665-.3-5.466-1.332-5.466-5.93 0-1.31.465-2.38 1.235-3.22-.135-.303-.54-1.523.105-3.176 0 0 1.005-.322 3.3 1.23.96-.267 1.98-.399 3-.405 1.02.006 2.04.138 3 .405 2.28-1.552 3.285-1.23 3.285-1.23.645 1.653.24 2.873.12 3.176.765.84 1.23 1.91 1.23 3.22 0 4.61-2.805 5.625-5.475 5.92.42.36.81 1.096.81 2.22 0 1.606-.015 2.896-.015 3.286 0 .315.21.69.825.57C20.565 22.092 24 17.592 24 12.297c0-6.627-5.373-12-12-12"/></svg></a><a class="VPSocialLink no-icon" href="https://twitter.com/andatoshiki" aria-label="twitter" target="_blank" rel="noopener" data-v-8a65be56 data-v-1b61e2c7><svg role="img" viewBox="0 0 24 24" xmlns="http://www.w3.org/2000/svg"><title>Twitter</title><path d="M21.543 7.104c.015.211.015.423.015.636 0 6.507-4.954 14.01-14.01 14.01v-.003A13.94 13.94 0 0 1 0 19.539a9.88 9.88 0 0 0 7.287-2.041 4.93 4.93 0 0 1-4.6-3.42 4.916 4.916 0 0 0 2.223-.084A4.926 4.926 0 0 1 .96 9.167v-.062a4.887 4.887 0 0 0 2.235.616A4.928 4.928 0 0 1 1.67 3.148 13.98 13.98 0 0 0 11.82 8.292a4.929 4.929 0 0 1 8.39-4.49 9.868 9.868 0 0 0 3.128-1.196 4.941 4.941 0 0 1-2.165 2.724A9.828 9.828 0 0 0 24 4.555a10.019 10.019 0 0 1-2.457 2.549z"/></svg></a><!--]--></div><div class="VPFlyout VPNavBarExtra extra" data-v-57f83237 data-v-e5c8c6ca data-v-62bba1f9><button type="button" class="button" aria-haspopup="true" aria-expanded="false" aria-label="extra navigation" data-v-62bba1f9><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" viewbox="0 0 24 24" class="icon" data-v-62bba1f9><circle cx="12" cy="12" r="2"></circle><circle cx="19" cy="12" r="2"></circle><circle cx="5" cy="12" r="2"></circle></svg></button><div class="menu" data-v-62bba1f9><div class="VPMenu" data-v-62bba1f9 data-v-17c3596a><!----><!--[--><!--[--><!----><div class="group" data-v-e5c8c6ca><div class="item appearance" data-v-e5c8c6ca><p class="label" data-v-e5c8c6ca>Appearance</p><div class="appearance-action" data-v-e5c8c6ca><button class="VPSwitch VPSwitchAppearance" type="button" role="switch" title="toggle dark mode" aria-checked="false" data-v-e5c8c6ca data-v-65b67168 data-v-56eb52d1><span class="check" data-v-56eb52d1><span class="icon" data-v-56eb52d1><!--[--><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" viewbox="0 0 24 24" class="sun" data-v-65b67168><path d="M12,18c-3.3,0-6-2.7-6-6s2.7-6,6-6s6,2.7,6,6S15.3,18,12,18zM12,8c-2.2,0-4,1.8-4,4c0,2.2,1.8,4,4,4c2.2,0,4-1.8,4-4C16,9.8,14.2,8,12,8z"></path><path d="M12,4c-0.6,0-1-0.4-1-1V1c0-0.6,0.4-1,1-1s1,0.4,1,1v2C13,3.6,12.6,4,12,4z"></path><path d="M12,24c-0.6,0-1-0.4-1-1v-2c0-0.6,0.4-1,1-1s1,0.4,1,1v2C13,23.6,12.6,24,12,24z"></path><path d="M5.6,6.6c-0.3,0-0.5-0.1-0.7-0.3L3.5,4.9c-0.4-0.4-0.4-1,0-1.4s1-0.4,1.4,0l1.4,1.4c0.4,0.4,0.4,1,0,1.4C6.2,6.5,5.9,6.6,5.6,6.6z"></path><path d="M19.8,20.8c-0.3,0-0.5-0.1-0.7-0.3l-1.4-1.4c-0.4-0.4-0.4-1,0-1.4s1-0.4,1.4,0l1.4,1.4c0.4,0.4,0.4,1,0,1.4C20.3,20.7,20,20.8,19.8,20.8z"></path><path d="M3,13H1c-0.6,0-1-0.4-1-1s0.4-1,1-1h2c0.6,0,1,0.4,1,1S3.6,13,3,13z"></path><path d="M23,13h-2c-0.6,0-1-0.4-1-1s0.4-1,1-1h2c0.6,0,1,0.4,1,1S23.6,13,23,13z"></path><path d="M4.2,20.8c-0.3,0-0.5-0.1-0.7-0.3c-0.4-0.4-0.4-1,0-1.4l1.4-1.4c0.4-0.4,1-0.4,1.4,0s0.4,1,0,1.4l-1.4,1.4C4.7,20.7,4.5,20.8,4.2,20.8z"></path><path d="M18.4,6.6c-0.3,0-0.5-0.1-0.7-0.3c-0.4-0.4-0.4-1,0-1.4l1.4-1.4c0.4-0.4,1-0.4,1.4,0s0.4,1,0,1.4l-1.4,1.4C18.9,6.5,18.6,6.6,18.4,6.6z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" viewbox="0 0 24 24" class="moon" data-v-65b67168><path d="M12.1,22c-0.3,0-0.6,0-0.9,0c-5.5-0.5-9.5-5.4-9-10.9c0.4-4.8,4.2-8.6,9-9c0.4,0,0.8,0.2,1,0.5c0.2,0.3,0.2,0.8-0.1,1.1c-2,2.7-1.4,6.4,1.3,8.4c2.1,1.6,5,1.6,7.1,0c0.3-0.2,0.7-0.3,1.1-0.1c0.3,0.2,0.5,0.6,0.5,1c-0.2,2.7-1.5,5.1-3.6,6.8C16.6,21.2,14.4,22,12.1,22zM9.3,4.4c-2.9,1-5,3.6-5.2,6.8c-0.4,4.4,2.8,8.3,7.2,8.7c2.1,0.2,4.2-0.4,5.8-1.8c1.1-0.9,1.9-2.1,2.4-3.4c-2.5,0.9-5.3,0.5-7.5-1.1C9.2,11.4,8.1,7.7,9.3,4.4z"></path></svg><!--]--></span></span></button></div></div></div><div class="group" data-v-e5c8c6ca><div class="item social-links" data-v-e5c8c6ca><div class="VPSocialLinks social-links-list" data-v-e5c8c6ca data-v-8a65be56><!--[--><a class="VPSocialLink no-icon" href="https://github.com/andatoshiki" aria-label="github" target="_blank" rel="noopener" data-v-8a65be56 data-v-1b61e2c7><svg role="img" viewBox="0 0 24 24" xmlns="http://www.w3.org/2000/svg"><title>GitHub</title><path d="M12 .297c-6.63 0-12 5.373-12 12 0 5.303 3.438 9.8 8.205 11.385.6.113.82-.258.82-.577 0-.285-.01-1.04-.015-2.04-3.338.724-4.042-1.61-4.042-1.61C4.422 18.07 3.633 17.7 3.633 17.7c-1.087-.744.084-.729.084-.729 1.205.084 1.838 1.236 1.838 1.236 1.07 1.835 2.809 1.305 3.495.998.108-.776.417-1.305.76-1.605-2.665-.3-5.466-1.332-5.466-5.93 0-1.31.465-2.38 1.235-3.22-.135-.303-.54-1.523.105-3.176 0 0 1.005-.322 3.3 1.23.96-.267 1.98-.399 3-.405 1.02.006 2.04.138 3 .405 2.28-1.552 3.285-1.23 3.285-1.23.645 1.653.24 2.873.12 3.176.765.84 1.23 1.91 1.23 3.22 0 4.61-2.805 5.625-5.475 5.92.42.36.81 1.096.81 2.22 0 1.606-.015 2.896-.015 3.286 0 .315.21.69.825.57C20.565 22.092 24 17.592 24 12.297c0-6.627-5.373-12-12-12"/></svg></a><a class="VPSocialLink no-icon" href="https://twitter.com/andatoshiki" aria-label="twitter" target="_blank" rel="noopener" data-v-8a65be56 data-v-1b61e2c7><svg role="img" viewBox="0 0 24 24" xmlns="http://www.w3.org/2000/svg"><title>Twitter</title><path d="M21.543 7.104c.015.211.015.423.015.636 0 6.507-4.954 14.01-14.01 14.01v-.003A13.94 13.94 0 0 1 0 19.539a9.88 9.88 0 0 0 7.287-2.041 4.93 4.93 0 0 1-4.6-3.42 4.916 4.916 0 0 0 2.223-.084A4.926 4.926 0 0 1 .96 9.167v-.062a4.887 4.887 0 0 0 2.235.616A4.928 4.928 0 0 1 1.67 3.148 13.98 13.98 0 0 0 11.82 8.292a4.929 4.929 0 0 1 8.39-4.49 9.868 9.868 0 0 0 3.128-1.196 4.941 4.941 0 0 1-2.165 2.724A9.828 9.828 0 0 0 24 4.555a10.019 10.019 0 0 1-2.457 2.549z"/></svg></a><!--]--></div></div></div><!--]--><!--]--></div></div></div><!--[--><!--]--><button type="button" class="VPNavBarHamburger hamburger" aria-label="mobile navigation" aria-expanded="false" aria-controls="VPNavScreen" data-v-57f83237 data-v-f865e4ad><span class="container" data-v-f865e4ad><span class="top" data-v-f865e4ad></span><span class="middle" data-v-f865e4ad></span><span class="bottom" data-v-f865e4ad></span></span></button></div></div></div></div><!----></header><div class="VPLocalNav reached-top" data-v-f6284a77 data-v-a41c4a1c><button class="menu" aria-expanded="false" aria-controls="VPSidebarNav" data-v-a41c4a1c><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" viewbox="0 0 24 24" class="menu-icon" data-v-a41c4a1c><path d="M17,11H3c-0.6,0-1-0.4-1-1s0.4-1,1-1h14c0.6,0,1,0.4,1,1S17.6,11,17,11z"></path><path d="M21,7H3C2.4,7,2,6.6,2,6s0.4-1,1-1h18c0.6,0,1,0.4,1,1S21.6,7,21,7z"></path><path d="M21,15H3c-0.6,0-1-0.4-1-1s0.4-1,1-1h18c0.6,0,1,0.4,1,1S21.6,15,21,15z"></path><path d="M17,19H3c-0.6,0-1-0.4-1-1s0.4-1,1-1h14c0.6,0,1,0.4,1,1S17.6,19,17,19z"></path></svg><span class="menu-text" data-v-a41c4a1c>Menu</span></button><div class="VPLocalNavOutlineDropdown" style="--vp-vh:0px;" data-v-a41c4a1c data-v-44ae7a43><button data-v-44ae7a43>Return to top</button><!----></div></div><aside class="VPSidebar" data-v-f6284a77 data-v-7ab77f34><div class="curtain" data-v-7ab77f34></div><nav class="nav" id="VPSidebarNav" aria-labelledby="sidebar-aria-label" tabindex="-1" data-v-7ab77f34><span class="visually-hidden" id="sidebar-aria-label" data-v-7ab77f34> Sidebar Navigation </span><!--[--><!--]--><!--[--><div class="group" data-v-7ab77f34><section class="VPSidebarItem level-0 collapsible has-active" data-v-7ab77f34 data-v-1b9f5c6f><div class="item" role="button" tabindex="0" data-v-1b9f5c6f><div class="indicator" data-v-1b9f5c6f></div><h2 class="text" data-v-1b9f5c6f>IPhO Formulas: JP Ver.</h2><div class="caret" role="button" aria-label="toggle section" tabindex="0" data-v-1b9f5c6f><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" viewbox="0 0 24 24" class="caret-icon" data-v-1b9f5c6f><path d="M9,19c-0.3,0-0.5-0.1-0.7-0.3c-0.4-0.4-0.4-1,0-1.4l5.3-5.3L8.3,6.7c-0.4-0.4-0.4-1,0-1.4s1-0.4,1.4,0l6,6c0.4,0.4,0.4,1,0,1.4l-6,6C9.5,18.9,9.3,19,9,19z"></path></svg></div></div><div class="items" data-v-1b9f5c6f><!--[--><div class="VPSidebarItem level-1 is-link" data-v-1b9f5c6f data-v-1b9f5c6f><div class="item" data-v-1b9f5c6f><div class="indicator" data-v-1b9f5c6f></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/1" data-v-1b9f5c6f><!--[--><p class="text" data-v-1b9f5c6f>1: 数学</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-1b9f5c6f data-v-1b9f5c6f><div class="item" data-v-1b9f5c6f><div class="indicator" data-v-1b9f5c6f></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/2" data-v-1b9f5c6f><!--[--><p class="text" data-v-1b9f5c6f>2: 一般的な推奨事</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-1b9f5c6f data-v-1b9f5c6f><div class="item" data-v-1b9f5c6f><div class="indicator" data-v-1b9f5c6f></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/3" data-v-1b9f5c6f><!--[--><p class="text" data-v-1b9f5c6f>3: 運動学</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-1b9f5c6f data-v-1b9f5c6f><div class="item" data-v-1b9f5c6f><div class="indicator" data-v-1b9f5c6f></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/4" data-v-1b9f5c6f><!--[--><p class="text" data-v-1b9f5c6f>4: 力学</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-1b9f5c6f data-v-1b9f5c6f><div class="item" data-v-1b9f5c6f><div class="indicator" data-v-1b9f5c6f></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/5" data-v-1b9f5c6f><!--[--><p class="text" data-v-1b9f5c6f>5: 振動と波</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-1b9f5c6f data-v-1b9f5c6f><div class="item" data-v-1b9f5c6f><div class="indicator" data-v-1b9f5c6f></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/6" data-v-1b9f5c6f><!--[--><p class="text" data-v-1b9f5c6f>6: 幾何光学，測光</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-1b9f5c6f data-v-1b9f5c6f><div class="item" data-v-1b9f5c6f><div class="indicator" data-v-1b9f5c6f></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/7" data-v-1b9f5c6f><!--[--><p class="text" data-v-1b9f5c6f>7: 波動光学</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-1b9f5c6f data-v-1b9f5c6f><div class="item" data-v-1b9f5c6f><div class="indicator" data-v-1b9f5c6f></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/8" data-v-1b9f5c6f><!--[--><p class="text" data-v-1b9f5c6f>8: 電気回路</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-1b9f5c6f data-v-1b9f5c6f><div class="item" data-v-1b9f5c6f><div class="indicator" data-v-1b9f5c6f></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/9" data-v-1b9f5c6f><!--[--><p class="text" data-v-1b9f5c6f>9: 電磁気学</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-1b9f5c6f data-v-1b9f5c6f><div class="item" data-v-1b9f5c6f><div class="indicator" data-v-1b9f5c6f></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/10" data-v-1b9f5c6f><!--[--><p class="text" data-v-1b9f5c6f>10: 熱力</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-1b9f5c6f data-v-1b9f5c6f><div class="item" data-v-1b9f5c6f><div class="indicator" data-v-1b9f5c6f></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/11" data-v-1b9f5c6f><!--[--><p class="text" data-v-1b9f5c6f>11: 量子力学</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-1b9f5c6f data-v-1b9f5c6f><div class="item" data-v-1b9f5c6f><div class="indicator" data-v-1b9f5c6f></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/12" data-v-1b9f5c6f><!--[--><p class="text" data-v-1b9f5c6f>12: Keplerの法則</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-1b9f5c6f data-v-1b9f5c6f><div class="item" data-v-1b9f5c6f><div class="indicator" data-v-1b9f5c6f></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/13" data-v-1b9f5c6f><!--[--><p class="text" data-v-1b9f5c6f>13: 相対性理論</p><!--]--></a><!----></div><!----></div><!--]--></div></section></div><!--]--><!--[--><!--]--></nav></aside><div class="VPContent has-sidebar" id="VPContent" data-v-f6284a77 data-v-f3ed2c70><div class="VPDoc has-sidebar has-aside" data-v-f3ed2c70 data-v-39e6c32d><!--[--><!--]--><div class="container" data-v-39e6c32d><div class="aside" data-v-39e6c32d><div class="aside-curtain" data-v-39e6c32d></div><div class="aside-container" data-v-39e6c32d><div class="aside-content" data-v-39e6c32d><div class="VPDocAside" data-v-39e6c32d data-v-f5b3965e><!--[--><!--]--><!--[--><!--]--><div class="VPDocAsideOutline" role="navigation" data-v-f5b3965e data-v-99fa007f><div class="content" data-v-99fa007f><div class="outline-marker" data-v-99fa007f></div><div class="outline-title" role="heading" aria-level="2" data-v-99fa007f>TOC</div><nav aria-labelledby="doc-outline-aria-label" data-v-99fa007f><span class="visually-hidden" id="doc-outline-aria-label" data-v-99fa007f> Table of Contents for current page </span><ul class="root" data-v-99fa007f data-v-29e3fa2f><!--[--><!--]--></ul></nav></div></div><!--[--><!--]--><div class="spacer" data-v-f5b3965e></div><!--[--><!--]--><!----><!--[--><!--]--><!--[--><!--[--><!--[--><!--[--><div class="VPDocAsideSponsors"><div class="VPSponsors vp-sponsor aside"><!--[--><section class="vp-sponsor-section"><!----><div class="VPSponsorsGrid vp-sponsor-grid medium"><!--[--><div class="vp-sponsor-grid-item"><a class="vp-sponsor-grid-link" target="_blank" rel="sponsored noopener"><article class="vp-sponsor-grid-box"><h4 class="visually-hidden"></h4><img class="vp-sponsor-grid-image" src="https://jsd.toshiki.dev/gh/andatoshiki/toshiki-notebook@master/assets/logo/sponsor/telegram.png"></article></a></div><!--]--></div></section><!--]--></div></div><!--]--><!--]--><!--]--><!--]--></div></div></div></div><div class="content" data-v-39e6c32d><div class="content-container" data-v-39e6c32d><!--[--><!--]--><!----><main class="main" data-v-39e6c32d><div style="position:relative;" class="vp-doc _academic_physics_ipho-formulas-jpn_10" data-v-39e6c32d><div><h1 id="formulas-for-ipho-日本語版-section-10" tabindex="-1">Formulas for IPhO 日本語版: Section 10 <a class="header-anchor" href="#formulas-for-ipho-日本語版-section-10" aria-label="Permalink to &quot;Formulas for IPhO 日本語版: Section 10&quot;">​</a></h1><div><section class="border-b-1 border-[var(--vp-c-divider)] w-full border-b-solid mt-[24px] pb-[12px] flex gap-[12px] mb-[12px] flex-wrap max-w-[85%]"><div class="flex gap-[4px] items-center"><svg style="display:inline-block;" viewBox="0 0 16 16" width="1.2em" height="1.2em"><path fill="currentColor" d="M8 16A8 8 0 1 1 8 0a8 8 0 0 1 0 16Zm.847-8.145a2.502 2.502 0 1 0-1.694 0C5.471 8.261 4 9.775 4 11c0 .395.145.995 1 .995h6c.855 0 1-.6 1-.995c0-1.224-1.47-2.74-3.153-3.145Z"></path></svg> Author:<span>Anda Toshiki</span></div><!----><div class="flex gap-[4px] items-center"><svg style="display:inline-block;" viewBox="0 0 15 15" width="1.2em" height="1.2em"><path fill="currentColor" fill-rule="evenodd" d="M1.903 7.297c0 3.044 2.207 5.118 4.686 5.547a.521.521 0 1 1-.178 1.027C3.5 13.367.861 10.913.861 7.297c0-1.537.699-2.745 1.515-3.663c.585-.658 1.254-1.193 1.792-1.602H2.532a.5.5 0 0 1 0-1h3a.5.5 0 0 1 .5.5v3a.5.5 0 0 1-1 0V2.686l-.001.002c-.572.43-1.27.957-1.875 1.638c-.715.804-1.253 1.776-1.253 2.97Zm11.108.406c0-3.012-2.16-5.073-4.607-5.533a.521.521 0 1 1 .192-1.024c2.874.54 5.457 2.98 5.457 6.557c0 1.537-.699 2.744-1.515 3.663c-.585.658-1.254 1.193-1.792 1.602h1.636a.5.5 0 1 1 0 1h-3a.5.5 0 0 1-.5-.5v-3a.5.5 0 1 1 1 0v1.845h.002c.571-.432 1.27-.958 1.874-1.64c.715-.803 1.253-1.775 1.253-2.97Z" clip-rule="evenodd"></path></svg> Updated:<span>a minute ago</span></div><div class="flex gap-[4px] items-center"><svg style="display:inline-block;" viewBox="0 0 16 16" width="1.2em" height="1.2em"><path fill="currentColor" d="M9.293 0H4a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h8a2 2 0 0 0 2-2V4.707A1 1 0 0 0 13.707 4L10 .293A1 1 0 0 0 9.293 0zM9.5 3.5v-2l3 3h-2a1 1 0 0 1-1-1zM5.485 6.879l1.036 4.144l.997-3.655a.5.5 0 0 1 .964 0l.997 3.655l1.036-4.144a.5.5 0 0 1 .97.242l-1.5 6a.5.5 0 0 1-.967.01L8 9.402l-1.018 3.73a.5.5 0 0 1-.967-.01l-1.5-6a.5.5 0 1 1 .97-.242z"></path></svg> Words:<span>613</span></div><div class="flex gap-[4px] items-center"><svg style="display:inline-block;" viewBox="0 0 20 20" width="1.2em" height="1.2em"><path fill="currentColor" d="M10 0a10 10 0 1 0 10 10A10 10 0 0 0 10 0zm2.5 14.5L9 11V4h2v6l3 3z"></path></svg> Reading:<span>3 min</span></div></section></div><h2 id="_10-熱力学" tabindex="-1">10: 熱力学 <a class="header-anchor" href="#_10-熱力学" aria-label="Permalink to &quot;10: 熱力学&quot;">​</a></h2><h3 id="_10-1" tabindex="-1">10.1: <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi>V</mi><mo>=</mo><mfrac><mi>w</mi><mi>M</mi></mfrac><mi>R</mi><mi>T</mi></mrow><annotation encoding="application/x-tex">p V=\frac{w}{M} R T</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">p</span><span class="mord mathnormal" style="margin-right:0.22222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0404em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6954em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">M</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02691em;">w</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord mathnormal" style="margin-right:0.13889em;">RT</span></span></span></span> <a class="header-anchor" href="#_10-1" aria-label="Permalink to &quot;10.1: $p V=\frac{w}{M} R T$&quot;">​</a></h3><ol><li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi>V</mi><mo>=</mo><mfrac><mi>w</mi><mi>M</mi></mfrac><mi>R</mi><mi>T</mi></mrow><annotation encoding="application/x-tex">p V=\frac{w}{M} R T</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">p</span><span class="mord mathnormal" style="margin-right:0.22222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0404em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6954em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">M</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02691em;">w</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord mathnormal" style="margin-right:0.13889em;">RT</span></span></span></span>.</li></ol><h3 id="_10-2-モルの気体の内部エネルギー" tabindex="-1">10.2: モルの気体の内部エネルギー <a class="header-anchor" href="#_10-2-モルの気体の内部エネルギー" aria-label="Permalink to &quot;10.2: モルの気体の内部エネルギー&quot;">​</a></h3><ol start="2"><li>1 モルの気体の内部エネルギー: <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>U</mi><mo>=</mo><mfrac><mi>i</mi><mn>2</mn></mfrac><mi>R</mi><mi>T</mi></mrow><annotation encoding="application/x-tex">U=\frac{i}{2} R T</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">U</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2007em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8557em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord mathnormal" style="margin-right:0.13889em;">RT</span></span></span></span> [訳者注: 単 原子分子理想気体 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi><mo>=</mo><mn>3</mn></mrow><annotation encoding="application/x-tex">i=3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6595em;"></span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">3</span></span></span></span>, 二原子分子理想気体 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi><mo>=</mo><mn>5</mn><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">i=5]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6595em;"></span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">5</span><span class="mclose">]</span></span></span></span>.</li></ol><h3 id="_10-3-標準状態" tabindex="-1">10.3: 標準状態 <a class="header-anchor" href="#_10-3-標準状態" aria-label="Permalink to &quot;10.3: 標準状態&quot;">​</a></h3><ol start="3"><li>標準状態での 1 モルの気体の体積は <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>22.4</mn><mrow><mtext> </mtext><mi mathvariant="normal">L</mi></mrow></mrow><annotation encoding="application/x-tex">22.4 \mathrm{~L}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">22.4</span><span class="mord"><span class="mspace nobreak"> </span><span class="mord mathrm">L</span></span></span></span></span>.</li></ol><h3 id="_10-4-断熱過程" tabindex="-1">10.4: 断熱過程 <a class="header-anchor" href="#_10-4-断熱過程" aria-label="Permalink to &quot;10.4: 断熱過程&quot;">​</a></h3><ol start="4"><li>断熱過程: 音速に比べて遅く, 熱の出入りがない. <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><msup><mi>V</mi><mi>γ</mi></msup><mo>=</mo></mrow><annotation encoding="application/x-tex">p V^\gamma=</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">p</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.22222em;">V</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05556em;">γ</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span></span></span></span> const. <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">(</mo><mi>T</mi><msup><mi>V</mi><mrow><mi>γ</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>=</mo></mrow><annotation encoding="application/x-tex">\left(T V^{\gamma-1}=\right.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2em;vertical-align:-0.35em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size1">(</span></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.22222em;">V</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.05556em;">γ</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mclose nulldelimiter"></span></span></span></span></span> const. <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mclose">)</span></span></span></span>.</li></ol><h3 id="_10-5-γ-cp-cv-i-2-i" tabindex="-1">10.5: γ=Cp/Cv=(i+2)/i <a class="header-anchor" href="#_10-5-γ-cp-cv-i-2-i" aria-label="Permalink to &quot;10.5: γ=Cp/Cv=(i+2)/i&quot;">​</a></h3><ol start="5"><li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>γ</mi><mo>=</mo><msub><mi>c</mi><mi>p</mi></msub><mi mathvariant="normal">/</mi><msub><mi>c</mi><mi>v</mi></msub><mo>=</mo><mo stretchy="false">(</mo><mi>i</mi><mo>+</mo><mn>2</mn><mo stretchy="false">)</mo><mi mathvariant="normal">/</mi><mi>i</mi></mrow><annotation encoding="application/x-tex">\gamma=c_p / c_v=(i+2) / i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.05556em;">γ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0361em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal">c</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mord">/</span><span class="mord"><span class="mord mathnormal">c</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03588em;">v</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mclose">)</span><span class="mord">/</span><span class="mord mathnormal">i</span></span></span></span>.</li></ol><h3 id="_10-6-boltzmann-分布" tabindex="-1">10.6: Boltzmann 分布 <a class="header-anchor" href="#_10-6-boltzmann-分布" aria-label="Permalink to &quot;10.6: Boltzmann 分布&quot;">​</a></h3><ol start="6"><li>Boltzmann 分布 :<p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>ρ</mi><mo>=</mo><msub><mi>ρ</mi><mn>0</mn></msub><msup><mi>e</mi><mrow><mo>−</mo><mi>M</mi><mi>g</mi><mi>h</mi><mi mathvariant="normal">/</mi><mi>R</mi><mi>T</mi></mrow></msup><mo>=</mo><msub><mi>ρ</mi><mn>0</mn></msub><msup><mi>e</mi><mrow><mo>−</mo><mi>U</mi><mi mathvariant="normal">/</mi><msub><mi>k</mi><mi>B</mi></msub><mi>T</mi></mrow></msup></mrow><annotation encoding="application/x-tex">\rho=\rho_0 e^{-M g h / R T}=\rho_0 e^{-U / k_B T} </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">ρ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.1324em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal">ρ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.938em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mathnormal mtight" style="margin-right:0.10903em;">M</span><span class="mord mathnormal mtight" style="margin-right:0.03588em;">g</span><span class="mord mathnormal mtight">h</span><span class="mord mtight">/</span><span class="mord mathnormal mtight" style="margin-right:0.13889em;">RT</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.1324em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal">ρ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.938em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mathnormal mtight" style="margin-right:0.10903em;">U</span><span class="mord mtight">/</span><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3567em;margin-left:-0.0315em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05017em;">B</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.1433em;"><span></span></span></span></span></span></span><span class="mord mathnormal mtight" style="margin-right:0.13889em;">T</span></span></span></span></span></span></span></span></span></span></span></span></span></p></li></ol><h3 id="_10-7-maxwell-分布" tabindex="-1">10.7: Maxwell 分布 <a class="header-anchor" href="#_10-7-maxwell-分布" aria-label="Permalink to &quot;10.7: Maxwell 分布&quot;">​</a></h3><ol start="7"><li>Maxwell 分布（v の速さをもつ分子の数）<div class="tip custom-block"><p class="custom-block-title">訳者注</p><p>位相空間で <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">v</mi></mrow><annotation encoding="application/x-tex">\boldsymbol{v}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4444em;"></span><span class="mord"><span class="mord"><span class="mord boldsymbol" style="margin-right:0.03704em;">v</span></span></span></span></span></span> と <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">v</mi><mo>+</mo><mi mathvariant="normal">d</mi><mi mathvariant="bold-italic">v</mi></mrow><annotation encoding="application/x-tex">\boldsymbol{v}+\mathrm{d} \boldsymbol{v}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord"><span class="mord"><span class="mord boldsymbol" style="margin-right:0.03704em;">v</span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathrm">d</span><span class="mord"><span class="mord"><span class="mord boldsymbol" style="margin-right:0.03704em;">v</span></span></span></span></span></span> の間にある分子の数の分布 であり，v の速さをもつ分子の数の分布とは異なる] <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∝</mo><msup><mi>e</mi><mrow><mo>−</mo><mi>m</mi><msup><mi mathvariant="bold-italic">v</mi><mn>2</mn></msup><mi mathvariant="normal">/</mi><mn>2</mn><msub><mi>k</mi><mi>B</mi></msub><mi>T</mi></mrow></msup></mrow><annotation encoding="application/x-tex">\propto e^{-m \boldsymbol{v}^2 / 2 k_B T}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mrel">∝</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.9869em;"></span><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9869em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mathnormal mtight">m</span><span class="mord mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord boldsymbol mtight" style="margin-right:0.03704em;">v</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8913em;"><span style="top:-2.931em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mord mtight">/2</span><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3567em;margin-left:-0.0315em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05017em;">B</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.1433em;"><span></span></span></span></span></span></span><span class="mord mathnormal mtight" style="margin-right:0.13889em;">T</span></span></span></span></span></span></span></span></span></span></span></span></p></div></li></ol><h3 id="_10-8-大気圧" tabindex="-1">10.8: 大気圧 <a class="header-anchor" href="#_10-8-大気圧" aria-label="Permalink to &quot;10.8: 大気圧&quot;">​</a></h3><ol start="8"><li>大気圧 : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mi>p</mi><mo>≪</mo><mi>p</mi></mrow><annotation encoding="application/x-tex">\Delta p \ll p</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord">Δ</span><span class="mord mathnormal">p</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≪</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">p</span></span></span></span> ならば <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mi>p</mi><mo>=</mo><mi>ρ</mi><mi>g</mi><mi mathvariant="normal">Δ</mi><mi>h</mi></mrow><annotation encoding="application/x-tex">\Delta p=\rho g \Delta h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord">Δ</span><span class="mord mathnormal">p</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">ρ</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord">Δ</span><span class="mord mathnormal">h</span></span></span></span>.</li></ol><h3 id="_10-9-公式" tabindex="-1">10.9: 公式 <a class="header-anchor" href="#_10-9-公式" aria-label="Permalink to &quot;10.9: 公式&quot;">​</a></h3><ol start="9"><li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mi>m</mi><mi>n</mi><mover accent="true"><msup><mi>v</mi><mn>2</mn></msup><mo stretchy="true">‾</mo></mover><mo>=</mo><mi>n</mi><msub><mi>k</mi><mi>B</mi></msub><mi>T</mi><mo stretchy="false">(</mo><mi>n</mi></mrow><annotation encoding="application/x-tex">p=\frac{1}{3} m n \overline{v^2}=n k_B T(n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">p</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2851em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">3</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord mathnormal">mn</span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9401em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.8601em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">n</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0315em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05017em;">B</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mopen">(</span><span class="mord mathnormal">n</span></span></span></span> は数密度 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">)</mo><mo separator="true">,</mo><msqrt><mover accent="true"><mover accent="true"><msup><mi>v</mi><mn>2</mn></msup><mo stretchy="true">‾</mo></mover><mo stretchy="true">‾</mo></mover></msqrt><mo>=</mo></mrow><annotation encoding="application/x-tex">), \sqrt{\overline{\overline{v^2}}}=</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.84em;vertical-align:-0.2849em;"></span><span class="mclose">)</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5551em;"><span class="svg-align" style="top:-3.8em;"><span class="pstrut" style="height:3.8em;"></span><span class="mord" style="padding-left:1em;"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.1401em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9401em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.8601em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span></span></span><span style="top:-4.0601em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span></span></span><span style="top:-3.5151em;"><span class="pstrut" style="height:3.8em;"></span><span class="hide-tail" style="min-width:1.02em;height:1.88em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.88em" viewBox="0 0 400000 1944" preserveAspectRatio="xMinYMin slice"><path d="M983 90
l0 -0
c4,-6.7,10,-10,18,-10 H400000v40
H1013.1s-83.4,268,-264.1,840c-180.7,572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7
s-12,0,-12,0c-1.3,-3.3,-3.7,-11.7,-7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744
c-10,12,-21,25,-33,39s-32,39,-32,39c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30
c26.7,-32.7,52,-63,76,-91s52,-60,52,-60s208,722,208,722
c56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5
c53.7,-170.3,84.5,-266.8,92.5,-289.5z
M1001 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2849em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span></span></span></span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msqrt><mrow><mn>3</mn><msub><mi>k</mi><mi>B</mi></msub><mi>T</mi><mi mathvariant="normal">/</mi><mi>m</mi></mrow></msqrt><mo separator="true">,</mo><mi>ν</mi><mo>=</mo><mi>v</mi><mi>n</mi><mi>S</mi></mrow><annotation encoding="application/x-tex">\sqrt{3 k_B T / m}, \nu=v n S</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.24em;vertical-align:-0.305em;"></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.935em;"><span class="svg-align" style="top:-3.2em;"><span class="pstrut" style="height:3.2em;"></span><span class="mord" style="padding-left:1em;"><span class="mord">3</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0315em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05017em;">B</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">/</span><span class="mord mathnormal">m</span></span></span><span style="top:-2.895em;"><span class="pstrut" style="height:3.2em;"></span><span class="hide-tail" style="min-width:1.02em;height:1.28em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.28em" viewBox="0 0 400000 1296" preserveAspectRatio="xMinYMin slice"><path d="M263,681c0.7,0,18,39.7,52,119
c34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120
c340,-704.7,510.7,-1060.3,512,-1067
l0 -0
c4.7,-7.3,11,-11,19,-11
H40000v40H1012.3
s-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232
c-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1
s-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26
c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z
M1001 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.305em;"><span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.06366em;">ν</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mord mathnormal">n</span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span></span></span></span>.</li></ol><h3 id="_10-10-carnot-サイクル" tabindex="-1">10.10: Carnot サイクル <a class="header-anchor" href="#_10-10-carnot-サイクル" aria-label="Permalink to &quot;10.10: Carnot サイクル&quot;">​</a></h3><ol start="10"><li>Carnot サイクル : 断熱過程 2 つと等温過程 2 つ. <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi><mo>−</mo><mi>T</mi></mrow><annotation encoding="application/x-tex">S-T</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span></span></span></span> 座標を用いることにより <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>η</mi><mo>=</mo><mrow><mo fence="true">(</mo><msub><mi>T</mi><mn>1</mn></msub><mo>−</mo><msub><mi>T</mi><mn>2</mn></msub><mo fence="true">)</mo></mrow><mi mathvariant="normal">/</mi><msub><mi>T</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">\eta=\left(T_1-T_2\right) / T_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">η</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;">)</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">/</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> を得る.</li></ol><h3 id="_10-11-ヒートポンプ" tabindex="-1">10.11: ヒートポンプ <a class="header-anchor" href="#_10-11-ヒートポンプ" aria-label="Permalink to &quot;10.11: ヒートポンプ&quot;">​</a></h3><ol start="11"><li>ヒートポンプ: Carnot サイクルの逆. <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>η</mi><mo>=</mo><mfrac><msub><mi>T</mi><mn>1</mn></msub><mrow><msub><mi>T</mi><mn>1</mn></msub><mo>−</mo><msub><mi>T</mi><mn>2</mn></msub></mrow></mfrac></mrow><annotation encoding="application/x-tex">\eta=\frac{T_1}{T_1-T_2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">η</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.3335em;vertical-align:-0.4451em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8884em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em;"><span style="top:-2.357em;margin-left:-0.1389em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mbin mtight">−</span><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em;"><span style="top:-2.357em;margin-left:-0.1389em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.4101em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em;"><span style="top:-2.357em;margin-left:-0.1389em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4451em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span>.</li></ol><h3 id="_10-12-エントロピー" tabindex="-1">10.12: エントロピー <a class="header-anchor" href="#_10-12-エントロピー" aria-label="Permalink to &quot;10.12: エントロピー&quot;">​</a></h3><ol start="12"><li>エントロピー <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>:</mo><mi mathvariant="normal">d</mi><mi>S</mi><mo>=</mo><mi mathvariant="normal">d</mi><mi>Q</mi><mi mathvariant="normal">/</mi><mi>T</mi></mrow><annotation encoding="application/x-tex">: \mathrm{d} S=\mathrm{d} Q / T</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathrm">d</span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathrm">d</span><span class="mord mathnormal">Q</span><span class="mord">/</span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span></span></span></span>.</li></ol><h3 id="_10-13-熱力学第一法則" tabindex="-1">10.13: 熱力学第一法則 <a class="header-anchor" href="#_10-13-熱力学第一法則" aria-label="Permalink to &quot;10.13: 熱力学第一法則&quot;">​</a></h3><ol start="13"><li>熱力学第一法則 : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="normal">d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mi>U</mi><mo>=</mo><msup><mi mathvariant="normal">d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mi>A</mi><mo>+</mo><msup><mi mathvariant="normal">d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mi>Q</mi></mrow><annotation encoding="application/x-tex">\mathrm{d}^{\prime} U=\mathrm{d}^{\prime} A+\mathrm{d}^{\prime} Q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7519em;"></span><span class="mord"><span class="mord mathrm">d</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7519em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.10903em;">U</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8352em;vertical-align:-0.0833em;"></span><span class="mord"><span class="mord mathrm">d</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7519em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.9463em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathrm">d</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7519em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mord mathnormal">Q</span></span></span></span></li></ol><h3 id="_10-14-熱力学第二法則" tabindex="-1">10.14: 熱力学第二法則 <a class="header-anchor" href="#_10-14-熱力学第二法則" aria-label="Permalink to &quot;10.14: 熱力学第二法則&quot;">​</a></h3><ol start="14"><li>熱力学第二法則 : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mi>S</mi><mo>≥</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">\Delta S \geq 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8193em;vertical-align:-0.136em;"></span><span class="mord">Δ</span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span> (また <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>η</mi><mtext>real </mtext></msub><mo>≤</mo><msub><mi>η</mi><mtext>Carnot </mtext></msub><mo fence="true">)</mo></mrow><annotation encoding="application/x-tex">\left.\eta_{\text {real }} \leq \eta_{\text {Carnot }}\right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="minner"><span class="mopen nulldelimiter"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">η</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">real </span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">η</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">Carnot </span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span>.</li></ol><h3 id="_10-15-気体のする仕事" tabindex="-1">10.15: 気体のする仕事 <a class="header-anchor" href="#_10-15-気体のする仕事" aria-label="Permalink to &quot;10.15: 気体のする仕事&quot;">​</a></h3><ol start="15"><li>気体のする仕事（<a href="./10#_10-10-carnot-サイクル">ポイント 10</a> も参照）:<p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>A</mi><mo>=</mo><mo>∫</mo><mi>p</mi><mrow><mtext> </mtext><mi mathvariant="normal">d</mi></mrow><mi>V</mi><mo separator="true">,</mo><mspace width="1em"></mspace><mtext> 断熱過程: </mtext><mi>A</mi><mo>=</mo><mfrac><mi>i</mi><mn>2</mn></mfrac><mi mathvariant="normal">Δ</mi><mo stretchy="false">(</mo><mi>p</mi><mi>V</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">A=\int p \mathrm{~d} V, \quad \text { 断熱過程: } A=\frac{i}{2} \Delta(p V) </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.2222em;vertical-align:-0.8622em;"></span><span class="mop op-symbol large-op" style="margin-right:0.44445em;position:relative;top:-0.0011em;">∫</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">p</span><span class="mord"><span class="mspace nobreak"> </span><span class="mord mathrm">d</span></span><span class="mord mathnormal" style="margin-right:0.22222em;">V</span><span class="mpunct">,</span><span class="mspace" style="margin-right:1em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord"> </span><span class="mord cjk_fallback">断熱過程</span><span class="mord">: </span></span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.0225em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3365em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord">Δ</span><span class="mopen">(</span><span class="mord mathnormal">p</span><span class="mord mathnormal" style="margin-right:0.22222em;">V</span><span class="mclose">)</span></span></span></span></span></p></li></ol><h3 id="_10-16-dalton-の法則" tabindex="-1">10.16: Dalton の法則 <a class="header-anchor" href="#_10-16-dalton-の法則" aria-label="Permalink to &quot;10.16: Dalton の法則&quot;">​</a></h3><ol start="16"><li><p>Dalton の法則: <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mo>=</mo></mrow><annotation encoding="application/x-tex">p=</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">p</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span></span></span></span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∑</mo><msub><mi>p</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">\sum p_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></p><div class="tip custom-block"><p class="custom-block-title">訳者注</p><p>理想気体のみ成立</p></div></li></ol><h3 id="_10-17-沸騰" tabindex="-1">10.17: 沸騰 <a class="header-anchor" href="#_10-17-沸騰" aria-label="Permalink to &quot;10.17: 沸騰&quot;">​</a></h3><ol start="17"><li>沸騰: 飽和蒸気の圧力 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>p</mi><mi>v</mi></msub><mo>=</mo><msub><mi>p</mi><mn>0</mn></msub><mi mathvariant="normal">.</mi><mn>2</mn></mrow><annotation encoding="application/x-tex">p_v=p_0 .2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03588em;">v</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord">.2</span></span></span></span> 液の界面では <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>p</mi><mrow><mi>v</mi><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>p</mi><mrow><mi>v</mi><mn>2</mn></mrow></msub><mo>=</mo><msub><mi>p</mi><mn>0</mn></msub></mrow><annotation encoding="application/x-tex">p_{v 1}+p_{v 2}=p_0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7778em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03588em;">v</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03588em;">v</span><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>.</li></ol><h3 id="_10-18-熱流" tabindex="-1">10.18: 熱流 <a class="header-anchor" href="#_10-18-熱流" aria-label="Permalink to &quot;10.18: 熱流&quot;">​</a></h3><ol start="18"><li>熱流: <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo>=</mo><mi>k</mi><mi>S</mi><mi mathvariant="normal">Δ</mi><mi>T</mi><mi mathvariant="normal">/</mi><mi>l</mi></mrow><annotation encoding="application/x-tex">P=k S \Delta T / l</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mord">Δ</span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">/</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span></span></span></span> ( <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">k</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span></span></span></span> は熱伝導率). 直流回路に似て いる <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>P</mi><mo>↔</mo><mi>I</mi><mo separator="true">,</mo><mi mathvariant="normal">Δ</mi><mi>T</mi><mo>↔</mo><mi>V</mi><mo separator="true">,</mo><mi>k</mi><mo>↔</mo><mn>1</mn><mi mathvariant="normal">/</mi><mi>ρ</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(P \leftrightarrow I, \Delta T \leftrightarrow V, k \leftrightarrow 1 / \rho)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">↔</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">Δ</span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">↔</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.22222em;">V</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">↔</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1/</span><span class="mord mathnormal">ρ</span><span class="mclose">)</span></span></span></span>.</li></ol><h3 id="_10-19-熱容量" tabindex="-1">10.19: 熱容量 <a class="header-anchor" href="#_10-19-熱容量" aria-label="Permalink to &quot;10.19: 熱容量&quot;">​</a></h3><ol start="19"><li>熱容量 : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Q</mi><mo>=</mo><mo>∫</mo><mi>c</mi><mo stretchy="false">(</mo><mi>T</mi><mo stretchy="false">)</mo><mi mathvariant="normal">d</mi><mi>T</mi></mrow><annotation encoding="application/x-tex">Q=\int c(T) \mathrm{d} T</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">Q</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.1111em;vertical-align:-0.3061em;"></span><span class="mop op-symbol small-op" style="margin-right:0.19445em;position:relative;top:-0.0006em;">∫</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">c</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mclose">)</span><span class="mord mathrm">d</span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span></span></span></span>. 固体では低温で <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>c</mi><mo>∝</mo><msup><mi>T</mi><mn>3</mn></msup></mrow><annotation encoding="application/x-tex">c \propto T^3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">c</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∝</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8141em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span></span></span></span></span></span></span></span>, 高温で <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>c</mi><mo>=</mo><mn>3</mn><mi>N</mi><msub><mi>k</mi><mi>B</mi></msub></mrow><annotation encoding="application/x-tex">c=3 N k_B</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">c</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8444em;vertical-align:-0.15em;"></span><span class="mord">3</span><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0315em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05017em;">B</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> （Dulong-Petit の法則. ここで <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>N</mi></mrow><annotation encoding="application/x-tex">N</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">N</span></span></span></span> は結晶中の原子数）</li></ol><h3 id="_10-20-表面張力" tabindex="-1">10.20: 表面張力 <a class="header-anchor" href="#_10-20-表面張力" aria-label="Permalink to &quot;10.20: 表面張力&quot;">​</a></h3><ol start="20"><li>表面張力 :<p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>U</mi><mo>=</mo><mi>S</mi><mi>σ</mi><mo separator="true">,</mo><mi>F</mi><mo>=</mo><mi>l</mi><mi>σ</mi><mo separator="true">,</mo><mi>p</mi><mo>=</mo><mn>2</mn><mi>σ</mi><mi mathvariant="normal">/</mi><mi>R</mi></mrow><annotation encoding="application/x-tex">U=S \sigma, F=l \sigma, p=2 \sigma / R </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">U</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">p</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span><span class="mord">/</span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span></span></span></span></span></p></li></ol><h3 id="_10-21-stefan-boltzmann-の法則-灰色体" tabindex="-1">10.21: Stefan-Boltzmann の法則 (灰色体) <a class="header-anchor" href="#_10-21-stefan-boltzmann-の法則-灰色体" aria-label="Permalink to &quot;10.21: Stefan-Boltzmann の法則 (灰色体)&quot;">​</a></h3><ol start="21"><li>Stefan-Boltzmann の法則 (灰色体) : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo>=</mo><mi>ε</mi><mi>σ</mi><mi>A</mi><msup><mi>T</mi><mn>4</mn></msup></mrow><annotation encoding="application/x-tex">P=\varepsilon \sigma A T^4</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8141em;"></span><span class="mord mathnormal">ε</span><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span><span class="mord mathnormal">A</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span></span></span></span></span></span></span></span>.</li></ol><h3 id="_10-22-wien-の変位則" tabindex="-1">10.22: Wien の変位則 <a class="header-anchor" href="#_10-22-wien-の変位則" aria-label="Permalink to &quot;10.22: Wien の変位則&quot;">​</a></h3><ol start="22"><li>Wien の変位則: <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>ν</mi><mi>max</mi><mo>⁡</mo></msub><mo>=</mo><mi>A</mi><msub><mi>k</mi><mi>B</mi></msub><mi>T</mi><mi mathvariant="normal">/</mi><mi>h</mi><mo stretchy="false">(</mo><mi>A</mi><mo>≈</mo></mrow><annotation encoding="application/x-tex">\nu_{\max }=A k_B T / h(A \approx</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.06366em;">ν</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0637em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mop mtight"><span class="mtight">m</span><span class="mtight">a</span><span class="mtight">x</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">A</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0315em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05017em;">B</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">/</span><span class="mord mathnormal">h</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span></span></span></span> 2.8), <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>λ</mi><mi>max</mi><mo>⁡</mo></msub><mo>=</mo><mi>h</mi><mi>c</mi><mi mathvariant="normal">/</mi><msup><mi>A</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><msub><mi>k</mi><mi>B</mi></msub><mi>T</mi><mrow><mo fence="true">(</mo><msup><mi>A</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo>≈</mo><mn>5</mn><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">\lambda_{\max }=h c / A^{\prime} k_B T\left(A^{\prime} \approx 5\right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8444em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">λ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mop mtight"><span class="mtight">m</span><span class="mtight">a</span><span class="mtight">x</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0019em;vertical-align:-0.25em;"></span><span class="mord mathnormal">h</span><span class="mord mathnormal">c</span><span class="mord">/</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7519em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0315em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05017em;">B</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7519em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">5</span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span>.</li></ol></div></div></main><footer class="VPDocFooter" data-v-39e6c32d data-v-bae355c8><!--[--><!--[--><!--[--><!--[--><!----><!--]--><!--]--><!--]--><!--]--><div class="edit-info" data-v-bae355c8><div class="edit-link" data-v-bae355c8><a class="VPLink link vp-external-link-icon no-icon edit-link-button" href="https://github.com/andatoshiki/toshiki-notebook/edit/master/docs/academic/physics/ipho-formulas-jpn/10.md" target="_blank" rel="noreferrer" data-v-bae355c8><!--[--><svg xmlns="http://www.w3.org/2000/svg" viewbox="0 0 24 24" class="edit-link-icon" aria-label="edit icon" data-v-bae355c8><path d="M18,23H4c-1.7,0-3-1.3-3-3V6c0-1.7,1.3-3,3-3h7c0.6,0,1,0.4,1,1s-0.4,1-1,1H4C3.4,5,3,5.4,3,6v14c0,0.6,0.4,1,1,1h14c0.6,0,1-0.4,1-1v-7c0-0.6,0.4-1,1-1s1,0.4,1,1v7C21,21.7,19.7,23,18,23z"></path><path d="M8,17c-0.3,0-0.5-0.1-0.7-0.3C7,16.5,6.9,16.1,7,15.8l1-4c0-0.2,0.1-0.3,0.3-0.5l9.5-9.5c1.2-1.2,3.2-1.2,4.4,0c1.2,1.2,1.2,3.2,0,4.4l-9.5,9.5c-0.1,0.1-0.3,0.2-0.5,0.3l-4,1C8.2,17,8.1,17,8,17zM9.9,12.5l-0.5,2.1l2.1-0.5l9.3-9.3c0.4-0.4,0.4-1.1,0-1.6c-0.4-0.4-1.2-0.4-1.6,0l0,0L9.9,12.5z M18.5,2.5L18.5,2.5L18.5,2.5z"></path></svg> Edit this page on GitHub<!--]--></a></div><div class="last-updated" data-v-bae355c8><p class="VPLastUpdated" data-v-bae355c8 data-v-ec8405ef>Last updated: <time datetime="2024-04-04T17:47:38.000Z" data-v-ec8405ef></time></p></div></div><nav class="prev-next" data-v-bae355c8><div class="pager" data-v-bae355c8><a class="pager-link prev" href="/academic/physics/ipho-formulas-jpn/9" data-v-bae355c8><span class="desc" data-v-bae355c8>Previous page</span><span class="title" data-v-bae355c8>9: 電磁気学</span></a></div><div class="pager" data-v-bae355c8><a class="pager-link next" href="/academic/physics/ipho-formulas-jpn/11" data-v-bae355c8><span class="desc" data-v-bae355c8>Next page</span><span class="title" data-v-bae355c8>11: 量子力学</span></a></div></nav></footer><!--[--><!--[--><!--[--><div id="comment-container"></div><!--]--><!--]--><!--]--></div></div></div><!--[--><!--]--></div></div><footer class="VPFooter has-sidebar" data-v-f6284a77 data-v-b69a1592><div class="container" data-v-b69a1592><p class="message" data-v-b69a1592>Wrote with <i class="heart fa fa-heart fa-xs fa-beat"></i> and <i class="coffee fa fa-coffee fa-xs" aria-hidden="true"></i> by <a href="https://toshiki.dev">Anda Toshiki</a> at <code>root@andatoshiki:/~</code></p><p class="copyright" data-v-b69a1592>Copyright © 2023-2024 <a href="https://github.com/andatoshiki">Anda Toshiki</a>, <a href="https://github.com/lolilab">LoliLab</a> and <a href="https://github.com/toshikidev">Toshiki Dev</a> present <br /><span id="siteruntime_span"></span></p></div></footer><!--[--><!--]--></div></div>
<script>window.__VP_HASH_MAP__=JSON.parse("{\"academic_chemistry_index.md\":\"3e9956c0\",\"academic_cis105_cis105-l9-lecture-note.md\":\"4cfc7d01\",\"academic_cis105_cis105-l1-lecture-note.md\":\"68a0a623\",\"academic_cis105_cis105-l12-lecture-note.md\":\"6c1923e8\",\"academic_chemistry_problems_03-02-3.md\":\"61bbe98d\",\"academic_cis105_cis105-l10-lecture-note.md\":\"3bcbe332\",\"academic_cis105_cis105-l13-lecture-note.md\":\"2612edc8\",\"academic_chemistry_problems_03-02-2.md\":\"dbf46ed7\",\"academic_cis105_cis105-l11-lecture-note.md\":\"025bcd90\",\"academic_cis105_cis105-l6-pt2-lecture-note.md\":\"307f8dc9\",\"academic_cis105_cis105-l7-lecture-note.md\":\"02e1ea20\",\"academic_cis105_cis105-l2-lecture-note.md\":\"fc69ba0b\",\"academic_cis105_cis105-l5-lecture-note.md\":\"0ec82392\",\"academic_cis105_cis105-l14-lecture-note.md\":\"d06cba8b\",\"academic_cis105_cis105-l3-lecture-note.md\":\"82a0e80e\",\"academic_cis105_cis105-l8-lecture-note.md\":\"524ae067\",\"academic_cis105_cis105-l4-lecture-note.md\":\"17e23954\",\"academic_cis105_cis105-l6-pt1-lecture-note.md\":\"296000a9\",\"academic_chemistry_problems_02-20.md\":\"b3d8bcf4\",\"academic_chemistry_problems_03-02-1.md\":\"7599caf1\",\"academic_chemistry_notes_12-5.md\":\"93b36153\",\"academic_physics_ipho-formulas-jpn_11.md\":\"a5458bf5\",\"application_markdown-it-katex_tips.md\":\"06781eb5\",\"application_vitepress-plugin-shiki-twoslash_api_includes.md\":\"e141e9e4\",\"application_vitepress-plugin-shiki-twoslash_api_logging.md\":\"93c47216\",\"application_vitepress-plugin-shiki-twoslash_api_annotations.md\":\"00836829\",\"application_vitepress-plugin-shiki-twoslash_api_emit.md\":\"fe47f2dc\",\"application_vitepress-plugin-shiki-twoslash_api_cutting.md\":\"5a958e10\",\"academic_physics_ipho-formulas-jpn_7.md\":\"9a351247\",\"academic_physics_index.md\":\"01e00528\",\"academic_literature_index.md\":\"e6586079\",\"academic_literature_writing_methods-of-development.md\":\"33d95b58\",\"application_vitepress-plugin-shiki-twoslash_api_multi-file.md\":\"405915b8\",\"application_vitepress-plugin-shiki-twoslash_api_errors.md\":\"13578fa2\",\"application_vitepress-plugin-shiki-twoslash_api_queries.md\":\"aaed9da6\",\"application_vitepress-plugin-shiki-twoslash_config_flags.md\":\"7617a4c4\",\"academic_physics_ipho-formulas-jpn_2.md\":\"1a994f7a\",\"academic_physics_ipho-formulas-jpn_12.md\":\"6ca71efc\",\"academic_vocabulary_index.md\":\"fa9b3324\",\"academic_physics_ipho-formulas-jpn_5.md\":\"c315066a\",\"application_vitepress-plugin-shiki-twoslash_api_types.md\":\"65f68a6e\",\"application_vitepress-plugin-shiki-twoslash_guide_markdown-extensions.md\":\"4ba62855\",\"academic_physics_ipho-formulas-jpn_10.md\":\"ebeb60b1\",\"academic_physics_ipho-formulas-jpn_6.md\":\"9df17b4f\",\"application_vitepress-plugin-shiki-twoslash_guide_custom-theme.md\":\"c8c6c9e5\",\"academic_physics_ipho-formulas-jpn_9.md\":\"b8cd6082\",\"academic_physics_ipho-formulas-jpn_3.md\":\"48226437\",\"academic_cis105_index.md\":\"34d38d4f\",\"academic_physics_ipho-formulas-jpn_8.md\":\"75906154\",\"application_markdown-it-katex_how-to-use.md\":\"4c7ef6ef\",\"development_aws_scientific-computing.md\":\"70353202\",\"development_aws_serverless.md\":\"8d5047d4\",\"development_aws_webserver.md\":\"dbc44335\",\"development_file-naming-convention.md\":\"8bc2c2ee\",\"development_git-push-authentication-failed.md\":\"0d60ec3a\",\"development_rclone-for-r2.md\":\"dc5f5c97\",\"development_proxy4shell-terminal.md\":\"2e781d39\",\"index.md\":\"7c63b214\",\"academic_physics_ipho-formulas-jpn_4.md\":\"d394e8ad\",\"javascript_notes_1_1-2.md\":\"11a4efd0\",\"jp_index.md\":\"9f899820\",\"save_reading_index.md\":\"2744abd4\",\"roadmap.md\":\"bec2e506\",\"javascript_notes_1_1-1.md\":\"a5aebdf4\",\"academic_physics_ipho-formulas-jpn_1.md\":\"06716568\",\"save_reading_outliers_3.md\":\"7d7443b7\",\"save_reading_outliers_2.md\":\"eab6bcd3\",\"save_reading_outliers_4.md\":\"2acad4bb\",\"development_aws_author.md\":\"5eb26574\",\"development_aws_handson-qabot.md\":\"9364f62f\",\"development_aws_aws-batch.md\":\"279b6b51\",\"development_aws_handson-serverless.md\":\"7c42a1fb\",\"development_aws_handson-jupyter.md\":\"e5c4e5e7\",\"save_reading_outliers_1.md\":\"aef7f35c\",\"development_aws_handson-bashoutter.md\":\"8c1f1c0e\",\"application_vitepress-plugin-shiki-twoslash_index.md\":\"13c8b731\",\"academic_vocabulary_2023_02_2023-02-27.md\":\"51648fcd\",\"application_vitepress-plugin-shiki-twoslash_config_reference.md\":\"64bb6664\",\"academic_physics_ipho-formulas-jpn_13.md\":\"a971f3ed\",\"development_aws_handson-ec2.md\":\"a6270935\",\"development_aws_appendix.md\":\"a5665141\",\"development_aws_assignments.md\":\"09fc7029\",\"development_aws_closing.md\":\"1db1f541\",\"development_aws_license.md\":\"6415dbdf\",\"development_aws_cloud.md\":\"8fc9562e\",\"development_aws_index.md\":\"07d91d22\",\"development_aws_acknowledgement.md\":\"d49de9db\",\"development_aws_aws-get-started.md\":\"e15efb52\",\"development_aws_docker-system.md\":\"b7f0145c\",\"development_aws_main.md\":\"bd2fe7d3\",\"application_markdown-it-katex_support-function.md\":\"a0659788\",\"application_markdown-it-katex_support-table.md\":\"6767ec07\"}");window.__VP_SITE_DATA__=JSON.parse("{\"lang\":\"en-US\",\"dir\":\"ltr\",\"title\":\"Toshiki's Note\",\"description\":\"Toshiki's web notebook served via Vitepress!\",\"base\":\"/\",\"head\":[],\"appearance\":true,\"themeConfig\":{\"nav\":[{\"text\":\"Development\",\"link\":\"/development/\"},{\"text\":\"Academic\",\"items\":[{\"text\":\"K-12\",\"items\":[{\"text\":\"Chemistry\",\"link\":\"/academic/chemistry/index\",\"activeMatch\":\"/academic/chemistry/\"},{\"text\":\"Discrete Math.\",\"link\":\"/discrete-math/index\",\"activeMatch\":\"/categories/fragments/\"},{\"text\":\"Literature\",\"link\":\"/academic/literature/index\",\"activeMatch\":\"/academic/literature/\"},{\"text\":\"CIS105\",\"link\":\"/academic/cis105/index\",\"activeMatch\":\"/academic/cis105/\"}]},{\"text\":\"Tools\",\"items\":[{\"text\":\"Formulas for IPhO JPN.\",\"link\":\"/academic/physics/ipho-formulas-jpn/1\",\"activeMatch\":\"/academic/physics/ipho-formulas-jpn/\"}]},{\"text\":\"\",\"link\":\"\",\"activeMatch\":\"\"},{\"text\":\"\",\"link\":\"\",\"activeMatch\":\"\"},{\"text\":\"\",\"link\":\"\",\"activeMatch\":\"\"},{\"text\":\"\",\"link\":\"\",\"activeMatch\":\"\"},{\"text\":\"\",\"link\":\"\",\"activeMatch\":\"\"},{\"text\":\"\",\"link\":\"\",\"activeMatch\":\"\"},{\"text\":\"\",\"link\":\"\",\"activeMatch\":\"\"}],\"activeMatch\":\"/academic/\"},{\"text\":\"Application\",\"items\":[{\"text\":\"Personal projects\",\"items\":[{\"text\":\"markdown-it-katex\",\"link\":\"/application/markdown-it-katex/how-to-use\",\"activeMatch\":\"/application/markdown-it-katex/\"},{\"text\":\"vitepress-plugin-shiki-twoslash\",\"link\":\"/application/vitepress-plugin-shiki-twoslash/index\",\"activeMatch\":\"/application/vitepress-plugin-shiki-twoslash/index\"}]}],\"activeMatch\":\"/save/\"},{\"text\":\"Save\",\"items\":[{\"text\":\"Reading\",\"link\":\"/save/reading/index\",\"activeMatch\":\"/save/reading/\"},{\"text\":\"Vocabulary\",\"link\":\"/academic/vocabulary/index\",\"activeMatch\":\"/academic/vocabulary/\"}],\"activeMatch\":\"/save/\"}],\"sidebar\":{\"/development/\":[{\"text\":\"Notes & Issues\",\"collapsed\":false,\"items\":[{\"text\":\"File Naming Convention\",\"link\":\"/development/file-naming-convention\"},{\"text\":\"RClone for R2\",\"link\":\"/development/rclone-for-r2\"},{\"text\":\"Proxies Configuration for Shells & Terminal\",\"link\":\"/development/proxy4shell-terminal\"},{\"text\":\"Git push results in \\\"Authentication Failed\\\"\",\"link\":\"/development/git-push-authentication-failed\"}]},{\"text\":\"コードで学ぶAWS入門\",\"collapsed\":false,\"items\":[{\"text\":\"背景\",\"link\":\"/development/aws/index\"},{\"text\":\"はじめに！\",\"link\":\"/development/aws/main\"},{\"text\":\"クラウド概論\",\"link\":\"/development/aws/cloud.md\"},{\"text\":\"AWS 入門\",\"link\":\"/development/aws/aws-get-started\"},{\"text\":\"Hands-on 1: 初めての EC2 インスタンスを起動する\",\"link\":\"/development/aws/handson-ec2.md\"},{\"text\":\"クラウドで行う科学計算・機械学習\",\"link\":\"/development/aws/scientific-computing.md\"},{\"text\":\"Hands-on 2: AWS でディープラーニングを実践\",\"link\":\"/development/aws/handson-ec2.md\"},{\"text\":\"Docker 入門\",\"link\":\"/development/aws/docker-system\"},{\"text\":\"Hands-on 3: AWS で自動質問回答ボットを走らせる\",\"link\":\"/development/aws/handson-qabot\"},{\"text\":\"Hands-on 4: AWS Batch を使って機械学習のハイパーパラメータサーチを並列化する\",\"link\":\"/development/aws/aws-batch\"},{\"text\":\"Web サービスの作り方\",\"link\":\"/development/aws/webserver\"},{\"text\":\"Serverless architecture\",\"link\":\"/development/aws/serverless\"},{\"text\":\"Hands-on 5: サーバーレス入門\",\"link\":\"/development/aws/handson-serverless\"},{\"text\":\"Hands-on 6: Bashoutter\",\"link\":\"/development/aws/handson-bashoutter\"},{\"text\":\"まとめ\",\"link\":\"/development/aws/closing\"},{\"text\":\"ppendix: 環境構築\",\"link\":\"/development/aws/appendix\"},{\"text\":\"謝辞\",\"link\":\"/development/aws/acknowledgement\"}]}],\"/academic/chemistry/\":[{\"text\":\"Textbook\",\"collapsed\":true,\"items\":[{\"text\":\"12-5: Reaction Mechanism\",\"link\":\"/academic/chemistry/notes/12-5\"},{\"text\":\"\",\"link\":\"\"},{\"text\":\"\",\"link\":\"\"},{\"text\":\"\",\"link\":\"\"},{\"text\":\"\",\"link\":\"\"},{\"text\":\"\",\"link\":\"\"},{\"text\":\"\",\"link\":\"\"},{\"text\":\"\",\"link\":\"\"}]},{\"text\":\"Kinetics\",\"collapsed\":false,\"items\":[{\"text\":\"Rate determining steps\",\"link\":\"/academic/chemistry/notes/kinetics/rate-determining-step\"},{\"text\":\"\",\"link\":\"\"},{\"text\":\"\",\"link\":\"\"},{\"text\":\"\",\"link\":\"\"}]},{\"text\":\"Problems & Solutions\",\"collapsed\":true,\"items\":[{\"text\":\"Problem: 02-20\",\"link\":\"/academic/chemistry/problems/02-20\"},{\"text\":\"Problem: 03-02-1\",\"link\":\"/academic/chemistry/problems/03-02-1\"},{\"text\":\"Problem: 03-02-2\",\"link\":\"/academic/chemistry/problems/03-02-2\"},{\"text\":\"Problem: 03-02-3\",\"link\":\"/academic/chemistry/problems/03-02-3\"}]}],\"/academic/physics\":[{\"text\":\"IPhO Formulas: JP Ver.\",\"collapsed\":false,\"items\":[{\"text\":\"1: 数学\",\"link\":\"/academic/physics/ipho-formulas-jpn/1\"},{\"text\":\"2: 一般的な推奨事\",\"link\":\"/academic/physics/ipho-formulas-jpn/2\"},{\"text\":\"3: 運動学\",\"link\":\"/academic/physics/ipho-formulas-jpn/3\"},{\"text\":\"4: 力学\",\"link\":\"/academic/physics/ipho-formulas-jpn/4\"},{\"text\":\"5: 振動と波\",\"link\":\"/academic/physics/ipho-formulas-jpn/5\"},{\"text\":\"6: 幾何光学，測光\",\"link\":\"/academic/physics/ipho-formulas-jpn/6\"},{\"text\":\"7: 波動光学\",\"link\":\"/academic/physics/ipho-formulas-jpn/7\"},{\"text\":\"8: 電気回路\",\"link\":\"/academic/physics/ipho-formulas-jpn/8\"},{\"text\":\"9: 電磁気学\",\"link\":\"/academic/physics/ipho-formulas-jpn/9\"},{\"text\":\"10: 熱力\",\"link\":\"/academic/physics/ipho-formulas-jpn/10\"},{\"text\":\"11: 量子力学\",\"link\":\"/academic/physics/ipho-formulas-jpn/11\"},{\"text\":\"12: Keplerの法則\",\"link\":\"/academic/physics/ipho-formulas-jpn/12\"},{\"text\":\"13: 相対性理論\",\"link\":\"/academic/physics/ipho-formulas-jpn/13\"}]}],\"/academic/cis105/\":[{\"text\":\"CIS 105: Computer Applications and Information Technology\",\"collapsed\":false,\"items\":[{\"text\":\"Course Overview & Schedule\",\"link\":\"/academic/cis105/index\"},{\"text\":\"Lect 1: Everything Changes\",\"link\":\"/academic/cis105/cis105-l1-lecture-note\"},{\"text\":\"Lect 2: Application Software\",\"link\":\"/academic/cis105/cis105-l2-lecture-note\"},{\"text\":\"Lect 3: Computer Hardware\",\"link\":\"/academic/cis105/cis105-l3-lecture-note\"},{\"text\":\"Lect 4: Formulas and Functions\",\"link\":\"/academic/cis105/cis105-l4-lecture-note\"},{\"text\":\"Lect 5: Operating System\",\"link\":\"/academic/cis105/cis105-l5-lecture-note\"},{\"text\":\"Lect 6 Pt 1: System Software\",\"link\":\"/academic/cis105/cis105-l6-pt1-lecture-note\"},{\"text\":\"Lect 6 Pt 2: Logical Functions\",\"link\":\"/academic/cis105/cis105-l6-pt2-lecture-note\"},{\"text\":\"Lect 7: Green Business Computing\",\"link\":\"/academic/cis105/cis105-l7-lecture-note\"},{\"text\":\"Lect 8: Green Computer Networks\",\"link\":\"/academic/cis105/cis105-l8-lecture-note\"},{\"text\":\"Lect 9: Internet\",\"link\":\"/academic/cis105/cis105-l9-lecture-note\"},{\"text\":\"Lect 10: Business Websites\",\"link\":\"/academic/cis105/cis105-l10-lecture-note\"},{\"text\":\"Lect 11: Computer Security\",\"link\":\"/academic/cis105/cis105-l11-lecture-note\"},{\"text\":\"Lect 12: Introduction to SQL\",\"link\":\"/academic/cis105/cis105-l12-lecture-note\"},{\"text\":\"Lect 13: Information Systems in Business\",\"link\":\"/academic/cis105/cis105-l13-lecture-note\"},{\"text\":\"Lect 14: More SQL Statements\",\"link\":\"/academic/cis105/cis105-l14-lecture-note\"}]}],\"/academic/vocabulary/\":[{\"text\":\"Vocabulary\",\"collapsed\":true,\"items\":[{\"text\":\"2023-02-27\",\"link\":\"/academic/vocabulary/2023/02/2023-02-27\"}]}],\"/academic/literature/\":[{\"text\":\"Writing Resources\",\"collapsed\":true,\"items\":[{\"text\":\"Patterns of Organization and Methods of Development\",\"link\":\"/academic/literature/writing/methods-of-development\"}]}],\"/javascript/\":[{\"text\":\"1: Basic JavaScript-Value, Variables, and Control Flow\",\"collapsed\":true,\"items\":[{\"text\":\"1-1: Numbers\",\"link\":\"/javascript/notes/1/1-1\"},{\"text\":\"\",\"link\":\"\"},{\"text\":\"\",\"link\":\"\"},{\"text\":\"\",\"link\":\"\"},{\"text\":\"\",\"link\":\"\"}]}],\"/save/reading/\":[{\"text\":\"Outliers\",\"collapsed\":true,\"items\":[{\"text\":\"Introduction & Chapter 1: The Roseto Mystery\",\"link\":\"/save/reading/outliers/1\"},{\"text\":\"Chapter 2: The 10,000-Hour Rule\",\"link\":\"/save/reading/outliers/2\"},{\"text\":\"Chapter 3: The Trouble with Geniuses, Part 1\",\"link\":\"/save/reading/outliers/3\"},{\"text\":\"Chapter 4: The Trouble with Geniuses, Part 2\",\"link\":\"/save/reading/outliers/4\"}]}],\"/application/markdown-it-katex/\":[{\"text\":\"markdown-it-katex\",\"collapsed\":false,\"items\":[{\"text\":\"1: How to use?\",\"link\":\"/application/markdown-it-katex/how-to-use\"},{\"text\":\"2: KaTeX supported functions\",\"link\":\"/application/markdown-it-katex/support-function\"},{\"text\":\"3: KaTeX support tables\",\"link\":\"/application/markdown-it-katex/support-table\"},{\"text\":\"4: Tips\",\"link\":\"/application/markdown-it-katex/tips\"}]}],\"/application/vitepress-plugin-shiki-twoslash/\":[{\"text\":\"Guide\",\"collapsed\":false,\"items\":[{\"text\":\"Getting Started\",\"link\":\"/application/vitepress-plugin-shiki-twoslash/\"},{\"text\":\"Markdown Extensions\",\"link\":\"/application/vitepress-plugin-shiki-twoslash/guide/markdown-extensions\"},{\"text\":\"Using a Custom Theme\",\"link\":\"/application/vitepress-plugin-shiki-twoslash/guide/custom-theme\"}]},{\"text\":\"Features\",\"collapsed\":false,\"items\":[{\"text\":\"Queries\",\"link\":\"/application/vitepress-plugin-shiki-twoslash/api/queries\"},{\"text\":\"Errors\",\"link\":\"/application/vitepress-plugin-shiki-twoslash/api/errors\"},{\"text\":\"Emit\",\"link\":\"/application/vitepress-plugin-shiki-twoslash/api/emit\"},{\"text\":\"Cutting\",\"link\":\"/application/vitepress-plugin-shiki-twoslash/api/cutting\"},{\"text\":\"Multi-file\",\"link\":\"/application/vitepress-plugin-shiki-twoslash/api/multi-file\"},{\"text\":\"@types\",\"link\":\"/application/vitepress-plugin-shiki-twoslash/api/types\"},{\"text\":\"Meta Annotations\",\"link\":\"/application/vitepress-plugin-shiki-twoslash/api/annotations\"},{\"text\":\"Logging\",\"link\":\"/application/vitepress-plugin-shiki-twoslash/api/logging\"},{\"text\":\"Includes\",\"link\":\"/application/vitepress-plugin-shiki-twoslash/api/includes\"}]},{\"text\":\"Config\",\"collapsed\":false,\"items\":[{\"text\":\"Reference\",\"link\":\"/application/vitepress-plugin-shiki-twoslash/config/reference\"},{\"text\":\"Compiler Flags\",\"link\":\"/application/vitepress-plugin-shiki-twoslash/config/flags\"}]}]},\"footer\":{\"copyright\":\"Copyright © 2023-2024 <a href=\\\"https://github.com/andatoshiki\\\">Anda Toshiki</a>, <a href=\\\"https://github.com/lolilab\\\">LoliLab</a> and <a href=\\\"https://github.com/toshikidev\\\">Toshiki Dev</a> present <br /><span id=\\\"siteruntime_span\\\"></span>\",\"message\":\"Wrote with <i class=\\\"heart fa fa-heart fa-xs fa-beat\\\"></i> and <i class=\\\"coffee fa fa-coffee fa-xs\\\" aria-hidden=\\\"true\\\"></i> by <a href=\\\"https://toshiki.dev\\\">Anda Toshiki</a> at <code>root@andatoshiki:/~</code>\"},\"logo\":\"/logos/logo.png\",\"outline\":\"deep\",\"outlineTitle\":\"TOC\",\"outlineBadges\":false,\"lastUpdatedText\":\"Last updated\",\"algolia\":{\"appId\":\"G9IUR45K98\",\"apiKey\":\"8528cc91281d8112b28f508317a96dd3\",\"indexName\":\"toshiki-notebook\"},\"editLink\":{\"pattern\":\"https://github.com/andatoshiki/toshiki-notebook/edit/master/docs/:path\",\"text\":\"Edit this page on GitHub\"},\"socialLinks\":[{\"icon\":\"github\",\"link\":\"https://github.com/andatoshiki\"},{\"icon\":\"twitter\",\"link\":\"https://twitter.com/andatoshiki\"}]},\"locales\":{\"/\":{\"label\":\"English\",\"lang\":\"en-US\"},\"/jp/\":{\"label\":\"Japanese\",\"title\":\"Vue Test Utils\",\"lang\":\"jp-JP\",\"description\":\"La documentation officielle de Vue Test Utils\"}},\"scrollOffset\":90,\"cleanUrls\":true}");</script>
</body>
</html>
Reference in New Issue View Git Blame Copy Permalink