{"id":17240,"date":"2010-12-04T14:02:05","date_gmt":"2010-12-04T06:02:05","guid":{"rendered":"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=17240"},"modified":"2021-10-06T16:30:22","modified_gmt":"2021-10-06T08:30:22","slug":"%e6%b0%a3%e9%ab%94%e5%8b%95%e5%8a%9b%e8%ab%96%e8%88%87%e6%96%b9%e5%9d%87%e6%a0%b9%e9%80%9f%e7%8e%87","status":"publish","type":"post","link":"http:\/\/localhost\/%e6%b0%a3%e9%ab%94%e5%8b%95%e5%8a%9b%e8%ab%96%e8%88%87%e6%96%b9%e5%9d%87%e6%a0%b9%e9%80%9f%e7%8e%87\/","title":{"rendered":"\u6c23\u9ad4\u52d5\u529b\u8ad6\u8207\u65b9\u5747\u6839\u901f\u7387"},"content":{"rendered":"

\u6c23\u9ad4\u52d5\u529b\u8ad6\u8207\u65b9\u5747\u6839\u901f\u7387<\/span>
\n\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><\/strong><\/p>\n

\u6211\u5011\u7531\u5fae\u89c0\u7684\u7c92\u5b50\u884c\u70ba\u89c0\u5bdf\u7406\u60f3\u6c23\u9ad4\u7684\u6027\u8cea\uff0c<\/p>\n

\u8a2d\u5728\u6b63\u7acb\u65b9\u9ad4\u5bb9\u5668\u4e2d\u88dd\u6709 $$n$$ \u83ab\u8033\u7406\u60f3\u6c23\u9ad4\uff0c\u5bb9\u5668\u7684\u908a\u9577 $$L$$\uff0c\u5167\u542b $$N$$ \u500b\u8cea\u91cf\u70ba $$m$$ \u7684\u76f8\u540c\u5206\u5b50\uff0c<\/p>\n

\u5247\u7b2c $$i$$ \u500b\u5206\u5b50\u649e\u64ca\u5668\u58c1\u7684\u52d5\u91cf\u8b8a\u5316\u91cf $$\\Delta \\vec{P_i}=-2mv_{ix}\\vec{i}$$\uff0c\u4f86\u56de\u4e00\u6b21\u82b1 $$\\Delta t_i=\\frac{2L}{v_{ix}}$$\uff0c<\/p>\n

\u56e0\u6b64\u7b2c $$i$$ \u500b\u5206\u5b50\u649e\u5176\u4e2d\u4e00\u9762($$A_x$$\u00a0\u9762)\u4e4b\u5e73\u5747\u529b $$\\vec{F_i}=\\displaystyle\\frac{\\Delta\\vec{P_i}}{\\Delta t_i}=\\frac{mv^2_{ix}}{L}\\vec{i}$$\uff0c<\/p>\n

\u56e0\u6b64\u5168\u90e8\u6c23\u9ad4\u649e $$A_x$$\u00a0\u9762\u7e3d\u529b $$\\displaystyle \\vec{F_x}=\\sum\\vec{F_i}=\\frac{m\\sum v^2_{ix}}{L}\\vec{i}$$<\/p>\n

\u53c8\u5047\u8a2d\u5206\u5b50\u649e\u64ca\u6bcf\u9762\u7684\u6a5f\u7387\u76f8\u7b49\uff0c\u56e0\u6b64<\/p>\n

$$\\displaystyle \\sum v^2_{ix}=\\sum v^2_{iy}=\\sum v^2_{iz}=\\frac{\\sum v^2_i}{3}$$<\/p>\n

$$\\displaystyle \\vec{F_x}=\\frac{m\\sum v^2_{ix}}{L}\\vec{i}=\\frac{M\\sum v^2_i}{3L}\\vec{i}$$<\/p>\n

\u5247 $$A_x$$ \u9762\u6240\u53d7\u4e4b\u58d3\u529b $$P:P=\\displaystyle\\frac{F_x}{L^2}=\\frac{m\\sum v^2_{ix}}{3L^3}=\\frac{mN\\overline{v}^2}{3V}$$<\/p>\n

$$\\displaystyle PV=\\frac{1}{3}mN\\overline{v}^2=\\frac{1}{3}Nmv^2_{rms}=\\frac{1}{3}nMv^2_{rms}$$\uff0c\u5176\u4e2d $$v_{rms}$$ \u7a31\u70ba\u65b9\u5747\u6839\u901f\u7387\uff0c$$M$$ \u70ba\u6c23\u9ad4\u4e4b\u5206\u5b50\u91cf\u3002<\/p>\n

\u9019\u544a\u8a34\u6211\u5011\u5de8\u89c0\u7684\u7269\u7406\u91cf\uff08\u58d3\u529b\uff09\u8207\u5fae\u89c0\u7269\u7406\u91cf\uff08\u5206\u5b50\u901f\u7387\uff09\u9593\u7684\u95dc\u4fc2\uff0c\u7531\u6b64\u53ef\u77e5\uff0c\u6c23\u9ad4\u58d3\u529b\u4f86\u6e90\u662f\u6c23\u9ad4\u5206\u5b50\u78b0\u649e\u7522\u751f\u3002\u5408\u4f75\u7406\u60f3\u6c23\u9ad4\u65b9\u7a0b\u5f0f\uff0c\u53ef\u5f97\u5206\u5b50\u4e4b\u65b9\u5747\u6839\u901f\u7387 $$v_{rms}=\\sqrt{\\overline{v}^2}=\\sqrt{\\frac{3RT}{M}}$$\u3002\u5728\u5ba4\u6eab $$(300K)$$ \u4e0b\uff0c\u6c2b\u6c23\u7684\u65b9\u5747\u6839\u901f\u7387\u7d04\u70ba $$1920~m\/s$$\uff0c\u800c\u6b64\u503c\u4e26\u975e\u6bcf\u500b\u6c23\u9ad4\u5206\u5b50\u7684\u901f\u7387\uff0c\u4e8b\u5be6\u4e0a\u6709\u4e9b\u5206\u5b50\u901f\u7387\u5927\u65bc\u6216\u662f\u5c0f\u65bc\u6b64\u503c\uff0c\u800c\u4e14\u5206\u5b50\u5728\u904b\u52d5\u7684\u540c\u6642\uff0c\u4e5f\u8207\u5176\u4ed6\u5206\u5b50\u4e0d\u505c\u7684\u78b0\u649e\uff0c\u56e0\u6b64\u5be6\u969b\u4e0a\u7684\u901f\u7387\u4e26\u975e\u5982\u7406\u8ad6\u503c\u9019\u9ebc\u5feb\u3002<\/p>\n

\n

\u53c3\u8003\u8cc7\u6599
\n<\/strong>1. David Halliday, Robert Resnick, Jearl Walker, \u666e\u901a\u7269\u7406\uff0c\u7b2c\u516b\u7248\uff0c2009\u5e742\u6708<\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"

\u6c23\u9ad4\u52d5\u529b\u8ad6\u8207\u65b9\u5747\u6839\u901f\u7387 \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 \u6211\u5011\u7531\u5fae\u89c0\u7684…<\/p>\n","protected":false},"author":50,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[18,16,107],"tags":[2204,2207,2205],"class_list":["post-17240","post","type-post","status-publish","format-standard","hentry","category-physics03-02","category-physics03","category-physics00","tag-2204","tag-2207","tag-2205","loop-entry","cat-18","cat-16","cat-107","no-thumbnail"],"views":29218,"_links":{"self":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/17240","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=17240"}],"version-history":[{"count":1,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/17240\/revisions"}],"predecessor-version":[{"id":89238,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/17240\/revisions\/89238"}],"wp:attachment":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/media?parent=17240"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/categories?post=17240"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/tags?post=17240"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}