{"id":17777,"date":"2010-12-08T17:41:46","date_gmt":"2010-12-08T09:41:46","guid":{"rendered":"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=17777"},"modified":"2021-10-06T16:30:20","modified_gmt":"2021-10-06T08:30:20","slug":"%e5%ae%9a%e5%ae%b9%e8%8e%ab%e8%80%b3%e6%af%94%e7%86%b1%e3%80%88constant-volume-processes-molar-specific-heat%e3%80%89","status":"publish","type":"post","link":"http:\/\/localhost\/%e5%ae%9a%e5%ae%b9%e8%8e%ab%e8%80%b3%e6%af%94%e7%86%b1%e3%80%88constant-volume-processes-molar-specific-heat%e3%80%89\/","title":{"rendered":"\u5b9a\u5bb9\u83ab\u8033\u6bd4\u71b1\u3008Constant-volume processes molar specific heat\u3009"},"content":{"rendered":"

\u5b9a\u5bb9\u83ab\u8033\u6bd4\u71b1\u3008Constant-volume processes molar specific heat\u3009
\n<\/span>\u81fa\u4e2d\u570b\u7acb\u65b0\u6e2f\u85dd\u8853\u9ad8\u7d1a\u4e2d\u5b78\u7269\u7406\u79d1\u7f85\u4f0a\u541b\u8001\u5e2b\/\u570b\u7acb\u5f70\u5316\u5e2b\u7bc4\u5927\u5b78\u5433\u4ef2\u537f\u6559\u6388\u8cac\u4efb\u7de8\u8f2f<\/span>
\n<\/strong>
\n\u71b1\u5b78\u7cfb\u7d71\u7684\u5167\u80fd\u70ba\u5167\u90e8\u5404\u5206\u5b50\u7684\u79fb\u52d5\u52d5\u80fd\u3001\u8f49\u52d5\u52d5\u80fd\u3001\u632f\u52d5\u52d5\u80fd\u548c\u5206\u5b50\u4e4b\u9593\u7684\u4f4d\u80fd\u7e3d\u548c\uff0c\u4f46\u56e0\u70ba\u55ae\u4e00\u539f\u5b50\uff08\u5982\uff1a\u6c26\uff09\u6c92\u6709\u8f49\u52d5\u52d5\u80fd\uff0c\u4e14\u6211\u5011\u5047\u5b9a\u7684\u7406\u60f3\u6c23\u9ad4\u5206\u5b50\u6578\u76ee\u975e\u5e38\u591a\uff0c\u5206\u5b50\u4e4b\u9593\u7684\u8ddd\u96e2\u751a\u9060\uff0c\u5206\u5b50\u4e4b\u9593\u7684\u4ea4\u4e92\u4f5c\u7528\u529b\u53ef\u4ee5\u5ffd\u7565\uff0c\u56e0\u6b64\u53ef\u5ffd\u7565\u5206\u5b50\u9593\u4f4d\u80fd\uff0c\u6240\u4ee5\u7406\u60f3\u6c23\u9ad4\u7684\u5167\u80fd\u50c5\u70ba\u6240\u6709\u5206\u5b50\u7684\u79fb\u52d5\u52d5\u80fd\uff0c\u4e5f\u5c31\u662f\u8cea\u5fc3\u52d5\u80fd\uff0c<\/p>\n

\u53c8\u4e00\u500b\u5206\u5b50\u5e73\u5747\u79fb\u52d5\u52d5\u80fd\u70ba $$E_k=\\displaystyle\\frac{3kT}{2}$$\uff08$$k$$ \u70ba\u6ce2\u8332\u66fc\u5e38\u6578\uff0c$$T$$ \u70ba\u7d55\u5c0d\u6eab\u5ea6\uff09\uff0c<\/p>\n

\u56e0\u6b64 $$n$$ \u83ab\u8033\u7684\u55ae\u539f\u5b50\u7406\u60f3\u6c23\u9ad4\u5167\u80fd\u5373\u70ba $$E_{int}=\\displaystyle(nN_A)\\frac{3}{2}kT=\\frac{3}{2}n(N_Ak)T=\\frac{3}{2}nRT$$<\/p>\n

\u5176\u4e2d $$N_A$$\u00a0\u70ba\u4e9e\u4f5b\u52a0\u53a5\u5e38\u6578\uff0c$$R$$ \u70ba\u7406\u60f3\u6c23\u9ad4\u5e38\u6578\uff0c$$T$$\u00a0\u70ba\u7d55\u5c0d\u6eab\u5ea6\u3002<\/p>\n

\u6211\u5011\u5047\u5b9a\u5728\u9ad4\u7a4d\u56fa\u5b9a\u70ba $$V$$ \u7684\u5bc6\u9589\u7cfb\u7d71\u4e2d\uff0c\u6709 $$n$$ \u83ab\u8033\u7684\u7406\u60f3\u6c23\u9ad4\uff0c\u7576\u6211\u5011\u7d66\u4e88\u71b1\u91cf $$Q$$ \u9032\u5165\u7cfb\u7d71\u4e2d\uff0c\u6c23\u9ad4\u6eab\u5ea6\u56e0\u800c\u589e\u52a0 $$\\Delta T$$\uff0c\u5247 $$Q=nC_V\\Delta T$$\uff0c$$C_V$$\u00a0\u70ba\u4e00\u500b\u5e38\u6578\uff0c\u7a31\u70ba\u5b9a\u5bb9\u83ab\u8033\u6bd4\u71b1\u3002<\/p>\n

\u6839\u64da\u71b1\u529b\u5b78\u7b2c\u4e00\u5b9a\u5f8b\uff0c$$\\Delta E_{int}=Q-W$$\uff08$$W$$ \u70ba\u7cfb\u7d71\u5c0d\u5916\u4f5c\u7684\u529f\uff09\uff0c\u7531\u65bc\u5728\u5c0d\u6c23\u9ad4\u52a0\u71b1\u904e\u7a0b\u4e2d\uff0c\u6c23\u9ad4\u9ad4\u7a4d\u7dad\u6301\u4e0d\u8b8a\uff0c\u56e0\u6b64\u7cfb\u7d71\u5c0d\u5916\u754c\u4f5c\u7684\u529f\u70ba\u96f6\uff0c\u4e5f\u5c31\u662f\u6c23\u9ad4\u81ea\u5916\u754c\u5438\u6536\u7684\u71b1\u91cf $$Q$$\uff0c\u5b8c\u5168\u8f49\u8b8a\u70ba\u7cfb\u7d71\u7684\u5167\u80fd $$E_{int}$$\uff0c\u56e0\u6b64<\/p>\n

$$\\displaystyle C_V=\\frac{\\Delta E_{int}}{n\\Delta T}~~~~~~~~~~(1)$$<\/p>\n

\u53c8 $$\\displaystyle E_{int}=\\frac{3}{2}nRT$$\uff0c\u56e0\u6b64\u00a0$$\\displaystyle \\Delta E_{int}=\\frac{3}{2}nR\\Delta T$$\uff0c<\/p>\n

\u4ee3\u5165 \u00a0$$(1)$$ \u5f0f\u5f97 $$\\displaystyle C_V=\\frac{3}{2}R=12.5~J\/mole\\cdot K$$<\/p>\n

\u4e0a\u5f0f\u9069\u7528\u65bc\u55ae\u539f\u5b50\u6c23\u9ad4\uff0c\u800c\u96d9\u539f\u5b50\u6c23\u9ad4\uff08\u5982\uff1a\u6c27\uff09\u53ca\u591a\u539f\u5b50\u6c23\u9ad4\uff08\u5982\uff1a\u7532\u70f7\uff09\u9664\u4e86\u79fb\u52d5\u52d5\u80fd\u5916\uff0c\u9084\u9700\u8003\u616e\u8f49\u52d5\u52d5\u80fd\u53ca\u632f\u52d5\u52d5\u80fd\uff0c\u6839\u64da\u99ac\u514b\u58eb\u5a01\u723e\u63d0\u51fa\u7684\u80fd\u91cf\u5747\u5206\u5b9a\u7406\uff0c\u4efb\u4e00\u7a2e\u5206\u5b50\u5132\u5b58\u80fd\u91cf\u7684\u65b9\u5f0f\u7a31\u70ba\u81ea\u7531\u5ea6\uff0c\u800c\u6bcf\u4e00\u500b\u81ea\u7531\u5ea6\u76f8\u7576\u65bc\u6bcf\u5206\u5b50\u5132\u5b58 $$\\frac{kT}{2}$$ \u7684\u80fd\u91cf\u3002<\/p>\n

\u5c0d\u5e73\u79fb\u800c\u8a00\uff0c\u7531\u65bc\u5206\u5b50\u5728\u4e00\u7a7a\u9593\u5167\u6709 $$x$$\u3001$$y$$\u3001$$z$$ \u4e09\u8ef8\u7684\u901f\u5ea6\u5206\u91cf\uff0c\u56e0\u6b64\u6709\u4e09\u500b\u5e73\u79fb\u7684\u81ea\u7531\u5ea6\uff0c\u56e0\u6b64\u5c0d\u61c9\u7684\u5206\u5b50\u5e73\u5747\u52d5\u80fd\u70ba $$2(\\frac{kT}{2})$$\uff0c\u800c\u5c0d\u96d9\u539f\u5b50\u5206\u5b50\u800c\u8a00\uff0c\u53e6\u6709\u5169\u500b\u65cb\u8f49\u81ea\u7531\u5ea6\uff0c\u56e0\u6b64\u96d9\u539f\u5b50\u5206\u5b50\u5177\u6709\u4e94\u500b\u81ea\u7531\u5ea6\uff0c\u4e5f\u5c31\u662f\u8aaa\uff0c\u96d9\u539f\u5b50\u5206\u5b50\u7684\u7e3d\u5167\u80fd\u70ba $$E_{int}=N5\\frac{kT}{2}=\\frac{5nRTE_{int}}{2}$$\uff08$$N$$ \u70ba\u5206\u5b50\u7e3d\u500b\u6578\uff09\uff0c\u56e0\u6b64\u96d9\u539f\u5b50\u6c23\u9ad4\u5206\u5b50\u7684\u5b9a\u5bb9\u83ab\u8033\u6bd4\u71b1 $$C_V=\\frac{5}{2}R=20.8~J\/mole\\cdot K$$<\/p>\n

\u53c3\u8003\u8cc7\u6599\uff1a<\/strong><\/p>\n

1. David Halliday, Robert Resnick, Jearl Walker, \u666e\u901a\u7269\u7406\uff08\u4e0a\uff09\u7b2c\u516b\u7248\uff0c2009\u5e742\u6708<\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"

\u5b9a\u5bb9\u83ab\u8033\u6bd4\u71b1\u3008Constant-volume processes molar specific heat\u3009 \u81fa…<\/p>\n","protected":false},"author":50,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[16,17,107],"tags":[2198,2197],"class_list":["post-17777","post","type-post","status-publish","format-standard","hentry","category-physics03","category-physics03-01","category-physics00","tag-2198","tag-2197","loop-entry","cat-16","cat-17","cat-107","no-thumbnail"],"views":20767,"_links":{"self":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/17777","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/users\/50"}],"replies":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/comments?post=17777"}],"version-history":[{"count":1,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/17777\/revisions"}],"predecessor-version":[{"id":89206,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/17777\/revisions\/89206"}],"wp:attachment":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/media?parent=17777"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/categories?post=17777"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/tags?post=17777"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}