{"id":30768,"date":"2021-05-07T13:00:02","date_gmt":"2021-05-07T13:00:02","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=30768"},"modified":"2025-01-01T18:57:05","modified_gmt":"2025-01-01T18:57:05","slug":"%e7%83%ad%e5%b9%b3%e8%a1%a1%e3%80%81%e6%b8%a9%e5%ba%a6%e5%8f%8a%e5%85%b6%e7%bb%9f%e8%ae%a1%e5%ae%9a%e4%b9%89","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/zh\/%e7%83%ad%e5%b9%b3%e8%a1%a1%e3%80%81%e6%b8%a9%e5%ba%a6%e5%8f%8a%e5%85%b6%e7%bb%9f%e8%ae%a1%e5%ae%9a%e4%b9%89\/","title":{"rendered":"\u70ed\u5e73\u8861\u3001\u6e29\u5ea6\u53ca\u5176\u7edf\u8ba1\u5b9a\u4e49"},"content":{"rendered":"<style>\n\tp, ul, ol {\n\t\ttext-align: justify;\n\t}\n\th1, h2 {\n\t\ttext-align: center;\n\t}\n<\/style>\n<h1>\u70ed\u5e73\u8861\u3001\u6e29\u5ea6\u53ca\u5176\u7edf\u8ba1\u5b9a\u4e49<\/h1>\n<p style=\"text-align: center\"><em>\u70ed\u529b\u5b66\u6e29\u5ea6\uff0c\u88ab\u7406\u89e3\u4e3a\u80fd\u91cf\u548c\u6982\u7387\u4e4b\u95f4\u7684\u8054\u7cfb\uff0c\u6e90\u4e8e\u70ed\u7cfb\u7edf\u4e2d\u5b8f\u89c2\u72b6\u6001\u4e0e\u5fae\u89c2\u72b6\u6001\u4e4b\u95f4\u7684\u5e73\u8861\u3002\u672c\u5185\u5bb9\u63a2\u8ba8\u4e86\u5982\u4f55\u901a\u8fc7\u6700\u5927\u5316\u5fae\u89c2\u72b6\u6001\u7684\u6570\u91cf\u6765\u5b9a\u4e49\u70ed\u5e73\u8861\uff0c\u5229\u7528\u6570\u5b66\u63a8\u5bfc\u548c\u7edf\u8ba1\u529b\u5b66\u6846\u67b6\u89e3\u91ca\u5176\u4e0e\u73bb\u5c14\u5179\u66fc\u5e38\u6570\u548c\u5f00\u5c14\u6587\u6e29\u6807\u7684\u5173\u7cfb\u3002<\/em><\/p>\n<p style=\"text-align: center;\"><strong>\u5b66\u4e60\u76ee\u6807\uff1a<\/strong><br \/>\n\u5b8c\u6210\u672c\u8282\u8bfe\u7a0b\u540e\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a\n<\/p>\n<ol>\n<li><strong>\u7406\u89e3<\/strong>\u70ed\u529b\u5b66\u7cfb\u7edf\u4e2d\u5b8f\u89c2\u72b6\u6001\u4e0e\u5fae\u89c2\u72b6\u6001\u4e4b\u95f4\u7684\u5173\u7cfb\u4ee5\u53ca\u6e29\u5ea6\u7684\u6982\u5ff5\u3002<\/li>\n<\/ol>\n<p style=\"text-align: center;\"><strong><u>\u5185\u5bb9\u76ee\u5f55<\/u>\uff1a<\/strong><br \/>\n<a href=\"#1\">\u70ed\u63a5\u89e6\u7cfb\u7edf\u7684\u5b8f\u89c2\u72b6\u6001\u4e0e\u5fae\u89c2\u72b6\u6001<\/a><br \/>\n<a href=\"#2\">\u70ed\u529b\u5b66\u6e29\u5ea6\uff1a\u5e73\u8861\u7cfb\u7edf\u7684\u5171\u540c\u5c5e\u6027<\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/7LPUN_vBoXE\" title=\"YouTube \u89c6\u9891\u64ad\u653e\u5668\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u70ed\u63a5\u89e6\u7cfb\u7edf\u7684\u5b8f\u89c2\u72b6\u6001\u4e0e\u5fae\u89c2\u72b6\u6001<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=7LPUN_vBoXE&amp;t=218s\" target=\"_blank\" rel=\"noopener\"><strong>\u8981\u63a2\u8ba8\u70ed\u529b\u5b66\u6e29\u5ea6\u7684\u6982\u5ff5<\/strong><\/a>\uff0c\u6211\u4eec\u9996\u5148\u9700\u8981\u4e86\u89e3\u70ed\u529b\u5b66\u7cfb\u7edf\u5982\u4f55\u76f8\u4e92\u4f5c\u7528\u53ca\u5176\u4e0e\u5b8f\u89c2\u72b6\u6001\u548c\u5fae\u89c2\u72b6\u6001\u7684\u5173\u7cfb\u3002\u8ba9\u6211\u4eec\u8003\u8651\u4e24\u4e2a\u5f7c\u6b64\u70ed\u63a5\u89e6\u4f46\u4e0e\u5916\u754c\u9694\u79bb\u7684\u7cfb\u7edf\u3002<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-kL0Rr2L4wys\/YJPlhBUTueI\/AAAAAAAAFEw\/OWpuyASOdGANXsSG5O-d09ed034DtMTuwCLcBGAsYHQ\/s0\/contacto%2Btermico.PNG\" alt=\"\u70ed\u63a5\u89e6\" class=\"aligncenter lazyload\" width=\"372\" height=\"158\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-kL0Rr2L4wys\/YJPlhBUTueI\/AAAAAAAAFEw\/OWpuyASOdGANXsSG5O-d09ed034DtMTuwCLcBGAsYHQ\/s0\/contacto%2Btermico.PNG\" alt=\"\u70ed\u63a5\u89e6\" class=\"aligncenter lazyload\" width=\"372\" height=\"158\" \/><\/noscript><\/p>\n<p>\u4e00\u65b9\u9762\uff0c\u7531\u4e8e\u7cfb\u7edf\u4fdd\u6301\u9694\u79bb\uff0c\u603b\u80fd\u91cf <span class=\"katex-eq\" data-katex-display=\"false\">E=E_1+E_2<\/span> \u662f\u6052\u5b9a\u7684\uff0c\u56e0\u6b64\u7cfb\u7edf\u7684\u5b8f\u89c2\u72b6\u6001\u53ef\u4ee5\u7531\u4ee5\u4e0b\u4e09\u79cd\u80fd\u91cf\u4e4b\u4e00\u6765\u5b9a\u4e49\uff1a<span class=\"katex-eq\" data-katex-display=\"false\">E, E_1<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">E_2<\/span>\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5982\u679c\u6211\u4eec\u8c08\u8bba\u5fae\u89c2\u72b6\u6001\uff0c\u80fd\u91cf\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">E_1<\/span> \u7684\u7cfb\u7edf\u6709 <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_1(E_1)<\/span> \u4e2a\u5fae\u89c2\u72b6\u6001\uff0c\u540c\u6837\uff0c\u80fd\u91cf\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">E_2<\/span> \u7684\u7cfb\u7edf\u6709 <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_2(E_2)<\/span> \u4e2a\u5fae\u89c2\u72b6\u6001\u3002\u56e0\u6b64\uff0c\u7ec4\u5408\u7cfb\u7edf\u5171\u6709 <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_1(E_1)\\Omega_2(E_2)<\/span> \u4e2a\u5fae\u89c2\u72b6\u6001\u3002<\/p>\n<h3>\u5173\u4e8e\u70ed\u529b\u5b66\u5e73\u8861\u7684\u5047\u8bbe<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=7LPUN_vBoXE&amp;t=392s\" target=\"_blank\" rel=\"noopener\"><strong>\u5982\u679c\u6bcf\u4e2a\u7cfb\u7edf\u90fd\u53ef\u4ee5\u4ea4\u6362\u80fd\u91cf<\/strong><\/a>\u76f4\u5230\u5b9e\u73b0<strong>\u70ed\u529b\u5b66\u5e73\u8861<\/strong>\uff0c\u5728\u67d0\u4e2a\u65f6\u523b <span class=\"katex-eq\" data-katex-display=\"false\">E_1<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">E_2<\/span> \u5c06\u8d8b\u4e8e\u7a33\u5b9a\u503c\u3002\u6b64\u65f6\u6211\u4eec\u9700\u8981\u7262\u8bb0\u7684\u5173\u952e\u601d\u60f3\u662f\uff0c\u6700\u6709\u53ef\u80fd\u53d1\u751f\u7684\u5b8f\u89c2\u72b6\u6001\u662f\u6700\u5927\u5316\u5fae\u89c2\u72b6\u6001\u6570\u91cf\u7684\u5b8f\u89c2\u72b6\u6001\u3002\u7531\u6b64\u5f97\u51fa\u4ee5\u4e0b\u5047\u8bbe\uff1a<\/p>\n<ol>\n<li>\u6bcf\u4e2a\u5fae\u89c2\u72b6\u6001\u53d1\u751f\u7684\u6982\u7387\u76f8\u540c\u3002<\/li>\n<li>\u7cfb\u7edf\u7684\u5185\u90e8\u52a8\u6001\u4f7f\u5f97\u5fae\u89c2\u72b6\u6001\u59cb\u7ec8\u5728\u4e0d\u65ad\u53d8\u5316\u3002<\/li>\n<li>\u7ecf\u8fc7\u4e00\u6bb5\u65f6\u95f4\u540e\uff0c\u7cfb\u7edf\u5c06\u63a2\u7d22\u6240\u6709\u53ef\u80fd\u7684\u5fae\u89c2\u72b6\u6001\uff0c\u5e76\u5728\u6bcf\u4e2a\u72b6\u6001\u4e2d\u505c\u7559\u76f8\u540c\u7684\u65f6\u95f4\u3002<\/li>\n<\/ol>\n<p>\u8fd9\u4e9b\u5047\u8bbe\u8868\u660e\uff0c\u7cfb\u7edf\u5c06\u5927\u90e8\u5206\u65f6\u95f4\u5904\u4e8e\u4ee3\u8868\u6700\u591a\u5fae\u89c2\u72b6\u6001\u7684\u5b8f\u89c2\u72b6\u6001\uff0c\u56e0\u6b64\u8fd9\u4e9b\u72b6\u6001\u662f\u6700\u53ef\u80fd\u7684\u3002\u5728\u901a\u5e38\u7814\u7a76\u7684\u70ed\u529b\u5b66\u7cfb\u7edf\u4e2d\uff0c\u201c\u6700\u53ef\u80fd\u201d\u8fd9\u4e00\u8868\u8fbe\u5b9e\u9645\u4e0a\u610f\u5473\u7740\u201c\u51e0\u4e4e\u7edd\u5bf9\u4e0d\u53ef\u80fd\u4e0d\u53d1\u751f\u201d\u3002\u8868\u9762\u4e0a\u770b\u8fd9\u662f\u4e00\u79cd\u7edf\u8ba1\u58f0\u660e\uff0c\u4f46\u5b9e\u9645\u4e0a\u5374\u51e0\u4e4e\u662f\u4e00\u4e2a\u786e\u5b9a\u6027\u7684\u7ed3\u8bba\u3002<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u70ed\u529b\u5b66\u6e29\u5ea6\uff1a\u5e73\u8861\u7cfb\u7edf\u7684\u5171\u540c\u5c5e\u6027<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=7LPUN_vBoXE&amp;t=617s\" target=\"_blank\" rel=\"noopener\"><strong>\u5bf9\u4e8e\u6211\u4eec\u6240\u8ba8\u8bba\u7684\u4e24\u4e2a\u7cfb\u7edf<\/strong><\/a>\u5728\u70ed\u63a5\u89e6\u4e2d\u7684\u95ee\u9898\uff0c\u6700\u53ef\u80fd\u7684\u80fd\u91cf\u5206\u5e03\u662f\u6700\u5927\u5316\u5fae\u89c2\u72b6\u6001\u6570\u91cf <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_1(E_1)\\Omega_2(E_2)<\/span> \u7684\u5206\u5e03\u3002\u7531\u4e8e\u7cfb\u7edf\u89c4\u6a21\u5de8\u5927\uff0c\u6211\u4eec\u53ef\u4ee5\u5229\u7528\u5fae\u79ef\u5206\u5de5\u5177\u4f5c\u4e3a\u826f\u597d\u7684\u8fd1\u4f3c\u6765\u63a8\u5bfc\u8fd9\u4e9b\u7ed3\u8bba\u7684\u542b\u4e49\u5e76\u63a8\u5bfc\u5176\u5c5e\u6027\u3002<\/p>\n<p>\u5982\u679c\u5bf9\u5176\u4e2d\u4e00\u4e2a\u7cfb\u7edf\u7684\u80fd\u91cf\u8fdb\u884c\u65e0\u7a77\u5c0f\u7684\u53d8\u5316\uff0c\u5e76\u5bfb\u627e\u4f7f\u5fae\u89c2\u72b6\u6001\u6570\u91cf\u6700\u5927\u5316\u7684\u60c5\u51b5\uff0c\u6211\u4eec\u5c06\u5f97\u5230\u4ee5\u4e0b\u63a8\u5bfc\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n(1) &amp; \\dfrac{d}{dE_1}\\left[  \\Omega_1(E_1) \\Omega_2(E_2) \\right] = 0 \\\\\n\n&amp; \\text{\uff1b\u56e0\u4e3a\u5fae\u89c2\u72b6\u6001\u6570\u91cf\u88ab\u6700\u5927\u5316} \\\\ \\\\\n\n\\equiv &amp; \\dfrac{d\\Omega_1(E_1)}{dE_1} \\Omega_2(E_2) + \\Omega_1(E_1) \\dfrac{d\\Omega_2(E_2)}{E_2}\\dfrac{dE_2}{dE_1} = 0 \\\\\n\n&amp; \\text{\uff1b\u5e94\u7528\u4e58\u79ef\u89c4\u5219\u548c\u94fe\u5f0f\u6cd5\u5219} \\\\ \\\\\n\n(2) &amp; E = E_1 + E_2 = \\text{\u5e38\u91cf} \\\\\n\n&amp; \\text{\uff1b\u70ed\u63a5\u89e6\u7cfb\u7edf\u7684\u603b\u80fd\u91cf} \\\\ \\\\\n\n\\equiv &amp; E_1 = E - E_2 \\\\ \\\\\n\n(3) &amp; \\dfrac{dE_2}{dE_1} = \\dfrac{d}{dE_1} (E - E_1) = -1\\;\\text{\uff1b\u7531 (2)} \\\\ \\\\\n\n(4) &amp; \\dfrac{d\\Omega_1}{dE_1}\\Omega_2 - \\Omega_2 \\dfrac{d\\Omega_2}{dE_2} = 0\\;\\text{\uff1b\u7531 (1) \u548c (3)} \\\\ \\\\\n\n\\equiv &amp; \\dfrac{d\\Omega_1}{dE_1} \\Omega_2 = \\Omega_1 \\dfrac{d\\Omega_2}{dE_2} \\\\ \\\\\n\n\\equiv &amp; \\dfrac{1}{\\Omega_1} \\dfrac{d\\Omega_1}{dE_1} = \\dfrac{1}{\\Omega_2} \\dfrac{d\\Omega_2}{dE_2} \\\\ \\\\\n\n\\equiv &amp; \\dfrac{d\\ln(\\Omega_1)}{dE_1} = \\dfrac{d\\ln(\\Omega_2)}{dE_2}\n\n\\end{array}<\/span>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u7406\u89e3\uff0c\u70ed\u5e73\u8861\u662f\u4e24\u4e2a\u7cfb\u7edf\u5728\u957f\u65f6\u95f4\u70ed\u63a5\u89e6\u4e2d\u6700\u53ef\u80fd\u7684\u5b8f\u89c2\u72b6\u6001\uff0c\u8fd9\u662f\u6700\u5927\u5316\u5fae\u89c2\u72b6\u6001\u6570\u91cf\u7684\u72b6\u6001\u3002\u5982\u679c\u53d1\u751f\u8fd9\u79cd\u60c5\u51b5\uff0c\u4ece\u4e0a\u8ff0\u63a8\u7406\u53ef\u4ee5\u5f97\u51fa\uff0c\u8fd9\u4e24\u4e2a\u7cfb\u7edf\u5b58\u5728\u4e00\u4e2a\u5171\u540c\u7684\u91cf\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a<strong>\u6e29\u5ea6<\/strong>\u3002<\/p>\n<h3>\u70ed\u529b\u5b66\u6e29\u5ea6\u7684\u5b9a\u4e49<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=7LPUN_vBoXE&amp;t=972s\" target=\"_blank\" rel=\"noopener\"><strong>\u5f53\u8fd9\u79cd\u60c5\u51b5\u53d1\u751f\u65f6\uff0c\u6211\u4eec\u8bf4\u4e24\u4e2a\u7cfb\u7edf<\/strong><\/a>\u201c\u5904\u4e8e\u76f8\u540c\u7684\u6e29\u5ea6\u201d\uff0c\u5e76\u5c06 <span class=\"katex-eq\" data-katex-display=\"false\">d\\ln\\Omega\/dE<\/span> \u4e0e\u6e29\u5ea6 <span class=\"katex-eq\" data-katex-display=\"false\">T<\/span> \u8054\u7cfb\u8d77\u6765\uff08\u5373 <span class=\"katex-eq\" data-katex-display=\"false\">T_1 = T_2<\/span>\uff09\u3002\u56e0\u6b64\uff0c\u70ed\u529b\u5b66\u6e29\u5ea6\u5b9a\u4e49\u4e3a\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{1}{k_B T} = \\frac{d\\ln\\Omega}{dE}<\/span>\n<p>\u5176\u4e2d <span class=\"katex-eq\" data-katex-display=\"false\">k_B=1.3807\\cdot 10^{-23}[J\/K]<\/span> \u662f<strong>\u73bb\u5c14\u5179\u66fc\u5e38\u6570<\/strong>\u3002<\/p>\n<p>\u901a\u8fc7\u8fd9\u79cd\u5e38\u6570\u7684\u9009\u62e9\uff0c\u6211\u4eec\u5b9a\u4e49\u7684\u6e29\u5ea6 <span class=\"katex-eq\" data-katex-display=\"false\">T<\/span> \u53ef\u4ee5\u83b7\u5f97\u5176\u901a\u5e38\u5728\u6211\u4eec\u6240\u77e5\u7684<strong>\u5f00\u5c14\u6587\u6e29\u6807<\/strong>\u4e2d\u7684\u89e3\u91ca\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u70ed\u5e73\u8861\u3001\u6e29\u5ea6\u53ca\u5176\u7edf\u8ba1\u5b9a\u4e49 \u70ed\u529b\u5b66\u6e29\u5ea6\uff0c\u88ab\u7406\u89e3\u4e3a\u80fd\u91cf\u548c\u6982\u7387\u4e4b\u95f4\u7684\u8054\u7cfb\uff0c\u6e90\u4e8e\u70ed\u7cfb\u7edf\u4e2d\u5b8f\u89c2\u72b6\u6001\u4e0e\u5fae\u89c2\u72b6\u6001\u4e4b\u95f4\u7684\u5e73\u8861\u3002\u672c\u5185\u5bb9\u63a2\u8ba8\u4e86\u5982\u4f55\u901a\u8fc7\u6700\u5927\u5316\u5fae\u89c2\u72b6\u6001\u7684\u6570\u91cf\u6765\u5b9a\u4e49\u70ed\u5e73\u8861\uff0c\u5229\u7528\u6570\u5b66\u63a8\u5bfc\u548c\u7edf\u8ba1\u529b\u5b66\u6846\u67b6\u89e3\u91ca\u5176\u4e0e\u73bb\u5c14\u5179\u66fc\u5e38\u6570\u548c\u5f00\u5c14\u6587\u6e29\u6807\u7684\u5173\u7cfb\u3002 \u5b66\u4e60\u76ee\u6807\uff1a 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