{"id":30069,"date":"2021-03-10T13:00:18","date_gmt":"2021-03-10T13:00:18","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=30069"},"modified":"2025-10-20T07:27:51","modified_gmt":"2025-10-20T07:27:51","slug":"%e7%90%86%e6%83%b3%e6%b0%94%e4%bd%93%e6%96%b9%e7%a8%8b","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/zh\/%e7%90%86%e6%83%b3%e6%b0%94%e4%bd%93%e6%96%b9%e7%a8%8b\/","title":{"rendered":"\u7406\u60f3\u6c14\u4f53\u65b9\u7a0b"},"content":{"rendered":"<style>\np, ul, ol{\n  text-align: justify;\n}\nh1{\n  text-align:center;\n  text-transform: uppercase;\n}\nh2{\n  text-align:center;\n  text-transform: uppercase;\n  font-size:24pt;\n}\nh3 { \n  text-align: center;\n  text-transform: uppercase;\n  font-size: 24px !important;\n}\n.example{\n  background:#f6f8fa; \n  border-left:4px solid #d00000; \n  padding:12px 14px; \n  margin:14px 0;\n}\n.small{\n  font-size: 0.95em;\n  color:#333;\n}\n<\/style>\n<h1>\u7406\u60f3\u6c14\u4f53\u7684\u7ecf\u9a8c\u516c\u5f0f<\/h1>\n<p style=\"text-align:center;\" dir=\"ltr\">\u4f60\u662f\u5426\u66fe\u7ecf\u60f3\u8fc7\uff0c\u4e3a\u4ec0\u4e48\u6c14\u7403\u5728\u52a0\u70ed\u65f6\u4f1a\u81a8\u80c0\uff0c\u6216\u8005\u4e3a\u4ec0\u4e48\u8f6e\u80ce\u7684\u538b\u529b\u4f1a\u968f\u7740\u9ad8\u5ea6\u7684\u53d8\u5316\u800c\u53d8\u5316\uff1f\u5728\u672c\u8bfe\u4e2d\uff0c\u6211\u4eec\u5c06\u56de\u987e\u652f\u914d\u8fd9\u4e9b\u73b0\u8c61\u7684\u89c4\u5f8b\uff0c\u4ee5\u53ca\u8fd9\u4e9b\u89c4\u5f8b\u5982\u4f55\u5f15\u5bfc\u6211\u4eec\u5f97\u5230\u7406\u60f3\u6c14\u4f53\u65b9\u7a0b\u5f0f\u3001\u5176\u8003\u91cf\u4e0e\u5173\u952e\u8981\u70b9\u3002<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><b>\u5b66\u4e60\u76ee\u6807<\/b><br \/>\n\u5b8c\u6210\u672c\u8bfe\u540e\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a<\/p>\n<ol>\n<li><b>\u89e3\u91ca<\/b>\u7406\u60f3\u6c14\u4f53\u7684\u7ecf\u9a8c\u5b9a\u5f8b\uff08\u6ce2\u4e49\u8033\u2013\u9a6c\u7565\u7279\u5b9a\u5f8b\u3001\u67e5\u7406\u5b9a\u5f8b\u3001\u76d6\u2013\u5415\u8428\u514b\u5b9a\u5f8b\uff09\u53ca\u5176\u5728\u72b6\u6001\u65b9\u7a0b\u4e2d\u7684\u7efc\u5408\u5f62\u5f0f\uff08<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">PV = nRT<\/span><\/span>, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">PV = N k_B T<\/span><\/span>\uff09\u3002<\/li>\n<li><b>\u5e94\u7528<\/b>\u7406\u60f3\u6c14\u4f53\u65b9\u7a0b\u53ca\u5173\u7cfb\u5f0f<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">PV\/T = cte<\/span><\/span>\u6765\u89e3\u51b3\u5177\u6709\u4e00\u81f4\u5355\u4f4d\u7684\u72b6\u6001\u53d8\u5316\u95ee\u9898\u3002<\/li>\n<li><b>\u5206\u6790<\/b>\u7b49\u6e29\u3001\u7b49\u538b\u4e0e\u7b49\u5bb9\u8fc7\u7a0b\u53ca\u5176\u5728<i>P\u2013V<\/i>\u3001<i>V\u2013T<\/i>\u548c<i>P\u2013T<\/i>\u56fe\u4e2d\u7684\u8f68\u8ff9\u3002<\/li>\n<li><b>\u8bc6\u522b<\/b>\u7406\u60f3\u6c14\u4f53\u7684\u9002\u7528\u8303\u56f4\uff0c\u5e76\u5728\u9002\u5f53\u60c5\u51b5\u4e0b\u9009\u62e9\u66ff\u4ee3\u6a21\u578b\uff08\u8303\u5fb7\u74e6\u5c14\u65af\u6a21\u578b\u3001\u91cf\u5b50\u6a21\u578b\u3001\u76f8\u5bf9\u8bba\u6a21\u578b\uff09\u3002<\/li>\n<\/ol>\n<p style=\"text-align:center;\" dir=\"ltr\">\n<b>\u5185\u5bb9\u76ee\u5f55<\/b><br \/>\n<a href=\"#1\">\u57fa\u672c\u7ecf\u9a8c\u5b9a\u5f8b<\/a><br \/>\n<a href=\"#2\">\u5c06\u5b9a\u5f8b\u7ec4\u5408\u4e3a\u7406\u60f3\u6c14\u4f53\u65b9\u7a0b<\/a><br \/>\n<a href=\"#3\">\u6309\u8fc7\u7a0b\u63a8\u5bfc<\/a><br \/>\n<a href=\"#4\">\u5fae\u89c2\u80cc\u666f\u4e0e\u8bf4\u660e<\/a><br \/>\n<a href=\"#5\">\u9002\u7528\u8303\u56f4\u4e0e\u5c40\u9650\u6027<\/a><br \/>\n<a href=\"#6\">\u5b9e\u8df5\u7b14\u8bb0<\/a>\n<\/p>\n<p><center><br \/>\n <iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/7WkrH_FS290?si=xWJQ-VAtbWgzm9bQ\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><br \/>\n<\/center><br \/>\n<a name=\"1\"><\/a><\/p>\n<h2>\u57fa\u672c\u7ecf\u9a8c\u5b9a\u5f8b<\/h2>\n<p>\u6c14\u4f53\u5b9e\u9a8c\u8868\u660e\uff0c\u538b\u529b <span class=\"katex-eq\" data-katex-display=\"false\">P<\/span>\u3001\u4f53\u79ef <span class=\"katex-eq\" data-katex-display=\"false\">V<\/span> \u548c\u6e29\u5ea6 <span class=\"katex-eq\" data-katex-display=\"false\">T<\/span> \u4e4b\u95f4\u5b58\u5728\u4f9d\u8d56\u5173\u7cfb\u3002\u5728\u53d7\u63a7\u6761\u4ef6\u4e0b\uff0c\u53ef\u4ee5\u89c2\u5bdf\u5230\u4e09\u6761\u57fa\u672c\u7ecf\u9a8c\u5b9a\u5f8b\uff1a<\/p>\n<ol>\n<li><strong>\u6ce2\u4e49\u8033\u2013\u9a6c\u7565\u7279\u5b9a\u5f8b\uff08\u7b49\u6e29\u8fc7\u7a0b\uff09\uff1a<\/strong> \u5728\u6052\u6e29\u8fc7\u7a0b\u4e2d\uff0c\u6c14\u4f53\u7684\u4f53\u79ef\u4e0e\u538b\u529b\u6210\u53cd\u6bd4\uff1b\u5373\uff1a\n<div style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P \\propto \\dfrac{1}{V}\\quad\\Leftrightarrow\\quad PV=\\text{cte.}<\/span><\/div>\n<div class=\"example\">\n  <strong>\u793a\u4f8b\uff1a<\/strong> \u4e00\u4e2a\u6c14\u4f53\u5728\u521d\u59cb\u538b\u529b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P_1 = 15\\ \\mathrm{MPa}<\/span><\/span> \u4e0b\uff0c\u7b49\u6e29\u81a8\u80c0\uff0c\u4ece\u521d\u59cb\u4f53\u79ef <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">V_1 = 1{,}00\\ \\mathrm{L}<\/span><\/span> \u5230\u6700\u7ec8\u4f53\u79ef <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">V_2 = 2{,}00\\ \\mathrm{L}<\/span><\/span>\uff0c\u5176\u538b\u529b\u5c06\u51cf\u534a\u3002\u7531\u4e8e\u4e58\u79ef <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">PV=\\text{cte.}<\/span><\/span> \u6052\u5b9a\uff0c\u56e0\u6b64\u6ee1\u8db3 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P_1 V_1 = P_2 V_2<\/span><\/span>\uff0c\u7531\u6b64\u5f97\u5230\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n  P_2 = \\dfrac{P_1 V_1}{V_2}\n\n      = 15\\ \\mathrm{MPa}\\left(\\dfrac{1{,}00\\ \\mathrm{L}}{2{,}00\\ \\mathrm{L}}\\right)\n\n      = 7{,}50\\ \\mathrm{MPa}\n\n  <\/span>\n<p>  <center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/pv-isotermico.jpg\" alt=\"\u7b49\u6e29\u8fc7\u7a0b\u7684 PV \u56fe\" width=\"480\" height=\"293\" class=\"aligncenter size-full wp-image-34975 lazyload\" \/><noscript><img decoding=\"async\" src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/pv-isotermico.jpg\" alt=\"\u7b49\u6e29\u8fc7\u7a0b\u7684 PV \u56fe\" width=\"480\" height=\"293\" class=\"aligncenter size-full wp-image-34975 lazyload\" srcset=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/pv-isotermico.jpg 480w, https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/pv-isotermico-300x183.jpg 300w\" sizes=\"(max-width: 480px) 100vw, 480px\" \/><\/noscript><\/center>\n<\/div>\n<\/li>\n<li><strong>\u67e5\u7406\u5b9a\u5f8b\uff08\u7b49\u538b\u8fc7\u7a0b\uff09\uff1a<\/strong> \u5728\u6052\u538b\u8fc7\u7a0b\u4e2d\uff0c\u6c14\u4f53\u7684\u4f53\u79ef\u4e0e\u6e29\u5ea6\u6210\u6b63\u6bd4\uff1b\u5373\uff1a\n<div style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">V \\propto T \\quad\\Leftrightarrow\\quad \\dfrac{V}{T}=\\text{cte.}<\/span><\/div>\n<div class=\"example\">\n  <strong>\u793a\u4f8b\uff1a<\/strong> \u4e00\u4e2a\u6c14\u4f53\u5728\u521d\u59cb\u6e29\u5ea6 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">T_1 = 300\\ \\mathrm{K}<\/span><\/span> \u4e0b\uff0c\u7b49\u538b\u52a0\u70ed\u81f3 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">T_2 = 450\\ \\mathrm{K}<\/span><\/span>\uff0c\u5176\u521d\u59cb\u4f53\u79ef\u4e3a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">V_1 = 2{,}00\\ \\mathrm{L}<\/span><\/span>\uff0c\u5176\u4f53\u79ef\u5c06\u589e\u52a0 50 %\uff08\u5373\u589e\u5927 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\tfrac{3}{2}<\/span><\/span> \u500d\uff09\u3002\u7531\u4e8e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\tfrac{V}{T}=\\text{cte.}<\/span><\/span> \u6052\u5b9a\uff0c\u56e0\u6b64\u6ee1\u8db3 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{V_1}{T_1}=\\dfrac{V_2}{T_2}<\/span><\/span>\uff0c\u7531\u6b64\u5f97\u5230\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n  V_2 = V_1 \\cdot \\dfrac{T_2}{T_1}\n\n      = 2{,}00\\ \\mathrm{L}\\left(\\dfrac{450\\ \\mathrm{K}}{300\\ \\mathrm{K}}\\right)\n\n      = 3{,}00\\ \\mathrm{L}\n\n  <\/span>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/isobara-proc.jpg\" alt=\"\" width=\"480\" height=\"298\" class=\"aligncenter size-full wp-image-34984 lazyload\" \/><noscript><img decoding=\"async\" src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/isobara-proc.jpg\" alt=\"\" width=\"480\" height=\"298\" class=\"aligncenter size-full wp-image-34984 lazyload\" srcset=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/isobara-proc.jpg 480w, https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/isobara-proc-300x186.jpg 300w\" sizes=\"(max-width: 480px) 100vw, 480px\" \/><\/noscript><\/center><\/p>\n<\/div>\n<\/li>\n<li><strong>\u76d6\u2013\u5415\u8428\u514b\u5b9a\u5f8b\uff08\u7b49\u5bb9\u8fc7\u7a0b\uff09\uff1a<\/strong> \u5728\u6052\u5bb9\u8fc7\u7a0b\u4e2d\uff0c\u6c14\u4f53\u7684\u538b\u529b\u4e0e\u6e29\u5ea6\u6210\u6b63\u6bd4\uff1b\u5373\uff1a\n<div style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P \\propto T \\quad\\Leftrightarrow\\quad \\dfrac{P}{T}=\\text{cte.}<\/span><\/div>\n<div class=\"example\">\n  <strong>\u793a\u4f8b\uff1a<\/strong> \u4e00\u4e2a\u6c14\u4f53\u5728\u521d\u59cb\u6e29\u5ea6 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">T_1 = 300\\ \\mathrm{K}<\/span><\/span> \u4e0b\uff0c\u7b49\u5bb9\u52a0\u70ed\u81f3 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">T_2 = 450\\ \\mathrm{K}<\/span><\/span>\uff0c\u5176\u521d\u59cb\u538b\u529b\u4e3a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P_1 = 1{,}00\\ \\mathrm{MPa}<\/span><\/span>\uff0c\u5176\u538b\u529b\u5c06\u6309\u76f8\u540c\u6bd4\u4f8b\u589e\u52a0\u3002\u7531\u4e8e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\tfrac{P}{T}=\\text{cte.}<\/span><\/span> \u6052\u5b9a\uff0c\u56e0\u6b64\u6ee1\u8db3 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{P_1}{T_1}=\\dfrac{P_2}{T_2}<\/span><\/span>\uff0c\u7531\u6b64\u5f97\u5230\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n  P_2 = P_1 \\cdot \\dfrac{T_2}{T_1}\n\n      = 1{,}00\\ \\mathrm{MPa}\\left(\\dfrac{450\\ \\mathrm{K}}{300\\ \\mathrm{K}}\\right)\n\n      = 1{,}50\\ \\mathrm{MPa}\n\n  <\/span>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/icororico-proc.jpg\" alt=\"\" width=\"480\" height=\"291\" class=\"aligncenter size-full wp-image-34987 lazyload\" \/><noscript><img decoding=\"async\" src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/icororico-proc.jpg\" alt=\"\" width=\"480\" height=\"291\" class=\"aligncenter size-full wp-image-34987 lazyload\" srcset=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/icororico-proc.jpg 480w, https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/icororico-proc-300x182.jpg 300w\" sizes=\"(max-width: 480px) 100vw, 480px\" \/><\/noscript><\/center>\n<\/div>\n<\/li>\n<\/ol>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u5c06\u5b9a\u5f8b\u7ec4\u5408\u4e3a\u7406\u60f3\u6c14\u4f53\u65b9\u7a0b<\/h2>\n<p>\u8fd9\u4e09\u6761\u5b9a\u5f8b\u53ef\u4ee5\u7efc\u5408\u4e3a\u4e00\u4e2a\u6bd4\u4f8b\u5173\u7cfb\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">PV \\propto T<\/span>\n<p>\u6839\u636e\u5b9e\u9a8c\u548c\u5fae\u89c2\u5206\u6790\uff0c\u53ef\u4ee5\u63a8\u5bfc\u51fa\u6bd4\u4f8b\u5e38\u6570\u4e3a\u7c92\u5b50\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">N<\/span> \u4e0e\u73bb\u5c14\u5179\u66fc\u5e38\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k_B = 1{,}380\\,649\\times10^{-23}\\ \\mathrm{J\\,K^{-1}}<\/span><\/span> \u7684\u4e58\u79ef\uff0c\u4ece\u800c\u5f97\u5230\u5fae\u89c2\u5173\u7cfb\u5f0f\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{PV = N\\,k_B\\,T}<\/span>\n<p>\u7c7b\u4f3c\u5730\uff0c\u5728\u6469\u5c14\u610f\u4e49\u4e0b\uff0c\u6bd4\u4f8b\u5e38\u6570\u7b49\u4e8e\u6469\u5c14\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u4e0e\u6c14\u4f53\u5e38\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">R=8{,}314\\,462\\,6\\ \\mathrm{J\\,mol^{-1}\\,K^{-1}}=0{,}082\\,057\\ \\mathrm{L\\,atm\\,mol^{-1}\\,K^{-1}}<\/span><\/span> \u7684\u4e58\u79ef\uff0c\u4ece\u800c\u5f97\u5230\u6469\u5c14\u5173\u7cfb\u5f0f\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{PV = n\\,R\\,T}<\/span>\n<p>\u65e0\u8bba\u54ea\u79cd\u60c5\u51b5\uff0c\u663e\u7136 <span class=\"katex-eq\" data-katex-display=\"false\">PV<\/span> \u4e0e <span class=\"katex-eq\" data-katex-display=\"false\">T<\/span> \u4e4b\u95f4\u5b58\u5728\u76f4\u63a5\u7684\u6b63\u6bd4\u5173\u7cfb\uff0c\u8fd9\u610f\u5473\u7740\u5982\u679c\u7406\u60f3\u6c14\u4f53\u4ece\u4e00\u4e2a\u72b6\u6001\uff08\u521d\u59cb\u503c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(P_\\alpha, V_\\alpha, T_\\alpha)<\/span><\/span>\uff09\u53d8\u5316\u5230\u53e6\u4e00\u4e2a\u72b6\u6001\uff08\u7ec8\u503c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(P_\\omega, V_\\omega, T_\\omega)<\/span><\/span>\uff09\uff0c\u5219\u6ee1\u8db3\u4ee5\u4e0b\u5173\u7cfb\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{P_\\alpha V_\\alpha}{T_\\alpha} =  \\dfrac{P_\\omega V_\\omega}{T_\\omega}<\/span>\n<p>\u56e0\u6b64\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">PV\/T = cte.<\/span><\/span><\/p>\n<p>\u8fd9\u4e00\u5173\u7cfb\u53ef\u4ee5\u4f5c\u4e3a\u5b9e\u9a8c\u57fa\u7840\uff0c\u7528\u4e8e\u63a8\u5bfc\u5fae\u89c2\u4e0e\u6469\u5c14\u5f62\u5f0f\u7684\u65b9\u7a0b\uff0c\u5b83\u53ef\u76f4\u63a5\u4ece\u6ce2\u4e49\u8033\u2013\u9a6c\u7565\u7279\u5b9a\u5f8b\u3001\u67e5\u7406\u5b9a\u5f8b\u548c\u76d6\u2013\u5415\u8428\u514b\u5b9a\u5f8b\u4e2d\u63a8\u5f97\u3002\u63a8\u7406\u5982\u4e0b\uff1a<\/p>\n<p>\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4e09\u79cd\u9014\u5f84\u6765\u8bc1\u660e\u8fd9\u4e00\u70b9\uff1a<\/p>\n<ol>\n<li><b>\u4f53\u79ef<\/b>\u53d8\u5316\uff1a\u7ecf\u7531\u7b49\u6e29\u8fc7\u7a0b\u4e0e\u7b49\u538b\u8fc7\u7a0b\u3002<\/li>\n<li><b>\u538b\u529b<\/b>\u53d8\u5316\uff1a\u7ecf\u7531\u7b49\u6e29\u8fc7\u7a0b\u4e0e\u7b49\u5bb9\u8fc7\u7a0b\u3002<\/li>\n<li><b>\u6e29\u5ea6<\/b>\u53d8\u5316\uff1a\u7ecf\u7531\u7b49\u538b\u8fc7\u7a0b\u4e0e\u7b49\u5bb9\u8fc7\u7a0b\u3002<\/li>\n<\/ol>\n<p>\u5728\u5206\u6790\u8fd9\u4e09\u79cd\u60c5\u51b5\u65f6\uff0c\u6211\u4eec\u9700\u8981\u4e00\u4e2a\u4e2d\u95f4\u72b6\u6001\uff0c\u5176\u53c2\u6570\u4e3a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(P_i,V_i,T_i)<\/span><\/span><\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>\u6309\u8fc7\u7a0b\u63a8\u5bfc<\/h2>\n<h3>\u6309\u4f53\u79ef\u53d8\u5316\u7684\u63a8\u5bfc<\/h3>\n<p>\u82e5\u521d\u59cb\u72b6\u6001 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(P_\\alpha,V_\\alpha,T_\\alpha)<\/span><\/span> \u901a\u8fc7\u7b49\u6e29\u8fc7\u7a0b\u8fde\u63a5\u81f3\u4e2d\u95f4\u72b6\u6001 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(P_i,V_i,T_i)<\/span><\/span>\uff0c\u518d\u7531\u7b49\u538b\u8fc7\u7a0b\u8fde\u63a5\u81f3\u6700\u7ec8\u72b6\u6001 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(P_\\omega,V_\\omega,T_\\omega)<\/span><\/span>\uff0c\u5219\u6709\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rclcl}\n\n &amp; P_\\alpha V_\\alpha= P_i V_i &amp; &amp; V_i\/T_i = V_\\omega\/T_\\omega   &amp; \\\\\n\n &amp;\\text{\u7b49\u6e29\u8fc7\u7a0b}&amp; &amp;\\text{\u7b49\u538b\u8fc7\u7a0b} &amp; \\\\\n\nP_\\alpha &amp; \\longrightarrow &amp; P_i = \\dfrac{P_\\alpha V_\\alpha}{V_i}  &amp; \\longrightarrow &amp; P_\\omega = P_i \\\\ \\\\\n\nV_\\alpha &amp; \\longrightarrow &amp; V_i = \\dfrac{P_\\alpha V_\\alpha}{P_i} &amp; \\longrightarrow &amp; V_\\omega = \\dfrac{V_i T_\\omega}{T_i} \\\\ \\\\\n\nT_\\alpha &amp; \\longrightarrow &amp; T_i = T_\\alpha &amp; \\longrightarrow &amp; T_\\omega = \\dfrac{V_\\omega T_i}{V_i}\n\n\\end{array}\n\n<\/span>\n<p>\u7531\u6b64\u53ef\u5f97\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n&amp; V_\\omega = \\left(\\dfrac{T_\\omega}{T_i}\\right) V_i = \\left(\\dfrac{T_\\omega}{T_i}\\right) \\left(\\dfrac{P_\\alpha}{P_i} \\right) V_\\alpha = \\dfrac{T_\\omega P_\\alpha V_\\alpha}{T_\\alpha P_\\omega} \\\\ \\\\\n\n\\equiv &amp; \\dfrac{P_\\alpha V_\\alpha}{T_\\alpha} = \\dfrac{P_\\omega V_\\omega}{T_\\omega}\n\n\\end{array}<\/span>\n<h3>\u6309\u538b\u529b\u53d8\u5316\u7684\u63a8\u5bfc<\/h3>\n<p>\u82e5\u521d\u59cb\u72b6\u6001 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(P_\\alpha,V_\\alpha,T_\\alpha)<\/span><\/span> \u901a\u8fc7\u7b49\u6e29\u8fc7\u7a0b\u8fde\u63a5\u81f3\u4e2d\u95f4\u72b6\u6001 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(P_i,V_i,T_i)<\/span><\/span>\uff0c\u7136\u540e\u7531\u7b49\u5bb9\u8fc7\u7a0b\u8fde\u63a5\u81f3\u6700\u7ec8\u72b6\u6001 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(P_\\omega,V_\\omega,T_\\omega)<\/span><\/span>\uff0c\u5219\u6709\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rclcl}\n\n &amp; P_\\alpha V_\\alpha= P_i V_i &amp; &amp; P_i\/T_i = P_\\omega\/T_\\omega   &amp; \\\\\n\n &amp;\\text{\u7b49\u6e29\u8fc7\u7a0b}&amp; &amp;\\text{\u7b49\u5bb9\u8fc7\u7a0b} &amp; \\\\\n\nP_\\alpha &amp; \\longrightarrow &amp; P_i = \\dfrac{P_\\alpha V_\\alpha}{V_i}  &amp; \\longrightarrow &amp; P_\\omega = \\dfrac{P_i T_\\omega}{T_i} \\\\ \\\\\n\nV_\\alpha &amp; \\longrightarrow &amp; V_i = \\dfrac{P_\\alpha V_\\alpha}{P_i} &amp; \\longrightarrow &amp; V_\\omega = V_i \\\\ \\\\\n\nT_\\alpha &amp; \\longrightarrow &amp; T_i = T_\\alpha &amp; \\longrightarrow &amp; T_\\omega = \\dfrac{V_\\omega T_i}{V_i}\n\n\\end{array}\n\n<\/span>\n<p>\u7531\u6b64\u53ef\u5f97\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n &amp; P_\\omega = \\left(\\dfrac{T_\\omega}{T_i}\\right) P_i = \\left(\\dfrac{T_\\omega}{T_i}\\right) \\left(\\dfrac{V_\\alpha}{V_i}\\right)P_\\alpha = \\dfrac{T_\\omega V_\\alpha P_\\alpha}{T_\\alpha V_\\omega} \\\\ \\\\\n\n\\equiv &amp; \\dfrac{P_\\alpha V_\\alpha}{T_\\alpha} = \\dfrac{P_\\omega V_\\omega}{T_\\omega}\n\n\\end{array}<\/span>\n<h3>\u6309\u6e29\u5ea6\u53d8\u5316\u7684\u63a8\u5bfc<\/h3>\n<p>\u82e5\u521d\u59cb\u72b6\u6001 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(P_\\alpha,V_\\alpha,T_\\alpha)<\/span><\/span> \u901a\u8fc7\u7b49\u538b\u8fc7\u7a0b\u8fde\u63a5\u81f3\u4e2d\u95f4\u72b6\u6001 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(P_i,V_i,T_i)<\/span><\/span>\uff0c\u7136\u540e\u7531\u7b49\u5bb9\u8fc7\u7a0b\u8fde\u63a5\u81f3\u6700\u7ec8\u72b6\u6001 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(P_\\omega,V_\\omega,T_\\omega)<\/span><\/span>\uff0c\u5219\u6709\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rclcl}\n\n &amp; V_\\alpha\/ T_\\alpha= V_i \/ T_i &amp; &amp; P_i\/T_i = P_\\omega\/T_\\omega   &amp; \\\\\n\n &amp;\\text{\u7b49\u538b\u8fc7\u7a0b}&amp; &amp;\\text{\u7b49\u5bb9\u8fc7\u7a0b} &amp; \\\\\n\nP_\\alpha &amp; \\longrightarrow &amp; P_i = P_\\alpha  &amp; \\longrightarrow &amp; P_\\omega = \\dfrac{P_i T_\\omega}{T_i} \\\\ \\\\\n\nV_\\alpha &amp; \\longrightarrow &amp; V_i = \\dfrac{V_\\alpha T_i}{T_\\alpha} &amp; \\longrightarrow &amp; V_\\omega = V_i \\\\ \\\\\n\nT_\\alpha &amp; \\longrightarrow &amp; T_i = \\dfrac{V_i T_\\alpha}{V_\\alpha} &amp; \\longrightarrow &amp; T_\\omega = \\dfrac{P_\\omega T_i}{P_i}\n\n\\end{array}\n\n<\/span>\n<p>\u7531\u6b64\u53ef\u5f97\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n &amp; T_\\omega = \\left(\\dfrac{P_\\omega}{P_i}\\right) T_i = \\left(\\dfrac{P_\\omega}{P_i}\\right) \\left(\\dfrac{V_i}{V_\\alpha}\\right)T_\\alpha = \\dfrac{P_\\omega V_\\omega T_\\alpha}{P_\\alpha V_\\alpha}  \\\\ \\\\\n\n\\equiv &amp; \\dfrac{P_\\alpha V_\\alpha}{T_\\alpha} = \\dfrac{P_\\omega V_\\omega}{T_\\omega}\n\n\\end{array}<\/span>\n<p><a name=\"4\"><\/a><\/p>\n<h2>\u8bc4\u8bba\u4e0e\u5fae\u89c2\u80cc\u666f<\/h2>\n<p>\u5c3d\u7ba1\u4e0a\u8ff0\u516c\u5f0f\u662f\u7ecf\u9a8c\u6027\u7684\uff0c\u4f46\u53ef\u901a\u8fc7\u6c14\u4f53\u52a8\u529b\u5b66\u7406\u8bba\u4ece\u7b2c\u4e00\u539f\u7406\u63a8\u5bfc\u51fa\u6765\u3002\u5728\u8be5\u6a21\u578b\u4e2d\uff0c\u6c14\u4f53\u88ab\u89c6\u4e3a\u7531\u5927\u91cf\u7c92\u5b50\u7ec4\u6210\u7684\u7cfb\u7edf\uff0c\u8fd9\u4e9b\u7c92\u5b50\u76f8\u4e92\u78b0\u649e\u5e76\u4e0e\u5bb9\u5668\u58c1\u78b0\u649e\u3002\u5176\u7406\u60f3\u5316\u5047\u8bbe\u5305\u62ec\uff1a<\/p>\n<ol>\n<li>\u7c92\u5b50\u4e4b\u95f4\u4e0d\u5b58\u5728\u8fdc\u7a0b\u7684\u5438\u5f15\u6216\u6392\u65a5\u529b\u3002<\/li>\n<li>\u7c92\u5b50\u662f\u70b9\u72b6\u7684\u6216\u4f53\u79ef\u53ef\u5ffd\u7565\u7684\u7403\u5f62\u9897\u7c92\u3002<\/li>\n<li>\u7c92\u5b50\u4e4b\u95f4\u53ca\u4e0e\u5bb9\u5668\u58c1\u7684\u78b0\u649e\u90fd\u662f\u5b8c\u5168\u5f39\u6027\u7684\u3002<\/li>\n<\/ol>\n<p>\u8fd9\u4e9b\u7406\u60f3\u5316\u7b80\u5316\u4e86\u5206\u6790\uff0c\u867d\u7136\u6ca1\u6709\u4efb\u4f55\u771f\u5b9e\u6c14\u4f53\u5b8c\u5168\u6ee1\u8db3\u8fd9\u4e9b\u6761\u4ef6\uff0c\u4f46\u5728\u8bb8\u591a\u6c14\u4f53\u7684\u5e7f\u6cdb\u6761\u4ef6\u4e0b\u4ecd\u80fd\u5f88\u597d\u5730\u63cf\u8ff0\u5176\u884c\u4e3a\uff0c\u5e76\u4e3a<strong>\u7ecf\u5178\u70ed\u529b\u5b66<\/strong>\u5960\u5b9a\u4e86\u57fa\u7840\uff0c\u5e94\u7528\u8303\u56f4\u6db5\u76d6\u4ece\u70ed\u673a\u5230\u5927\u6c14\u7269\u7406\u4e0e\u5929\u4f53\u7269\u7406\u7b49\u9886\u57df\u3002<\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u9002\u7528\u8303\u56f4\u4e0e\u5c40\u9650\u6027<\/h2>\n<p>\u7406\u60f3\u6c14\u4f53\u5b9a\u5f8b\u5e76\u975e\u666e\u9002\u3002\u5f53\u4e0a\u8ff0\u5047\u8bbe\u4e0d\u518d\u5408\u7406\u6216\u51fa\u73b0\u8d85\u51fa\u7ecf\u5178\u7269\u7406\u8303\u56f4\u7684\u6548\u5e94\u65f6\uff0c\u5b83\u4f1a\u4ea7\u751f\u504f\u79bb\u3002<\/p>\n<ul>\n<li><strong>\u9ad8\u538b\u4e0e\u4f4e\u6e29\uff1a<\/strong>\u5206\u5b50\u95f4\u76f8\u4e92\u4f5c\u7528\u4e0d\u518d\u53ef\u5ffd\u7565\uff0c\u7c92\u5b50\u7684\u6709\u9650\u4f53\u79ef\u5f00\u59cb\u663e\u8457\u3002\u5e38\u89c1\u7684\u4fee\u6b63\u5f62\u5f0f\u662f\u8303\u5fb7\u74e6\u5c14\u65af\u65b9\u7a0b\uff1a\n<div style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(P + a\\left(\\dfrac{n}{V}\\right)^2\\right)\\,(V - nb)=nRT<\/span><\/div>\n<p>    \u5176\u4e2d <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u662f\u5404\u6c14\u4f53\u7279\u6709\u7684\u53c2\u6570\u3002\n  <\/li>\n<li><strong>\u91cf\u5b50\u533a\u95f4\uff1a<\/strong>\u5728\u6781\u4f4e\u6e29\u6216\u9ad8\u5bc6\u5ea6\u6761\u4ef6\u4e0b\uff0c\u7c92\u5b50\u9075\u5faa\u73bb\u8272\u2013\u7231\u56e0\u65af\u5766\u6216\u8d39\u7c73\u2013\u72c4\u62c9\u514b\u7edf\u8ba1\uff0c\u9700\u8981\u91c7\u7528<em>\u91cf\u5b50\u6c14\u4f53<\/em>\u6a21\u578b\u3002<\/li>\n<li><strong>\u76f8\u5bf9\u8bba\u533a\u95f4\uff1a<\/strong>\u5f53\u7c92\u5b50\u901f\u5ea6\u63a5\u8fd1\u5149\u901f\u65f6\uff0c\u9700\u8981\u5f15\u5165\u76f8\u5bf9\u8bba\u4fee\u6b63\u3002<\/li>\n<\/ul>\n<p><a name=\"6\"><\/a><\/p>\n<h2>\u5b9e\u7528\u8bf4\u660e<\/h2>\n<ul>\n<li>\u5728\u516c\u5f0f\u4e2d\u5e94\u59cb\u7ec8\u4f7f\u7528<strong>\u5f00\u5c14\u6587\u6e29\u5ea6<\/strong>\uff1a<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">T(\\mathrm{K}) = T(^{\\circ}\\mathrm{C}) + 273{,}15<\/span><\/span>\u3002<\/li>\n<li>\u4fdd\u6301\u5355\u4f4d\u4e00\u81f4\u6027\uff1a\u82e5\u4f7f\u7528 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{atm}<\/span><\/span> \u4e0e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{L}<\/span><\/span>\uff0c\u5219\u91c7\u7528 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">R=0{,}082\\,057\\ \\mathrm{L\\,atm\\,mol^{-1}\\,K^{-1}}<\/span><\/span>\uff1b\u82e5\u4f7f\u7528 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{Pa}<\/span><\/span> \u4e0e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{m^3}<\/span><\/span>\uff0c\u5219\u91c7\u7528 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">R=8{,}314\\,462\\,6\\ \\mathrm{J\\,mol^{-1}\\,K^{-1}}<\/span><\/span>\u3002<\/li>\n<li>\u8bf7\u8bb0\u4f4f\uff0c\u6bcf\u6761\u7ecf\u9a8c\u5b9a\u5f8b\u90fd\u662f\u5728\u4fdd\u6301\u4e00\u4e2a\u53d8\u91cf\u4e0d\u53d8\u7684\u60c5\u51b5\u4e0b\u5f97\u51fa\u7684\u3002\u8981\u7ed3\u5408\u7ed3\u679c\uff0c\u5fc5\u987b\u660e\u786e\u6bcf\u4e2a\u9636\u6bb5\u8fdb\u884c\u7684\u70ed\u529b\u5b66\u8fc7\u7a0b\u3002<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u7406\u60f3\u6c14\u4f53\u7684\u7ecf\u9a8c\u516c\u5f0f 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