\u7406\u60f3\u6c17\u4f53\u306e\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u3092\u8868\u3059\u30b6\u30c3\u30af\u30fc\u30eb\u30fb\u30c6\u30c8\u30ed\u30fc\u30c7\u65b9\u7a0b\u5f0f\u306f\u53e4\u5178\u7d71\u8a08\u529b\u5b66\u304b\u3089\u6c42\u3081\u3089\u308c\u307e\u3057\u305f\u3002<\/p>\n\n\n\n
\u3057\u304b\u3057\u79c1\u305f\u3061\u306f\u5206\u5b50\u306e\u6319\u52d5\u3092\u8868\u3059\u306b\u306f\u91cf\u5b50\u529b\u5b66\u3092\u4f7f\u308f\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u3053\u3068\u3092\u77e5\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n
\u3068\u3044\u3046\u3053\u3068\u3067\u3001\u30b7\u30e5\u30ec\u30c7\u30a3\u30f3\u30ac\u30fc\u65b9\u7a0b\u5f0f\u304b\u3089\u51fa\u767a\u3057\u3066\u30b6\u30c3\u30af\u30fc\u30eb\u30fb\u30c6\u30c8\u30ed\u30fc\u30c7\u65b9\u7a0b\u5f0f\u3092\u307f\u3061\u3073\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n
\u3068\u306f\u3044\u3048\u6700\u521d\u304b\u3089\u8a08\u7b97\u3059\u308b\u3068\u9577\u304f\u306a\u308b\u3060\u3051\u306a\u306e\u3067\u4e95\u6238\u578b\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u3067\u306e\u89e3\u304c\u308f\u304b\u3063\u3066\u3044\u308b\u524d\u63d0\u3067\u9032\u3081\u307e\u3059\u3002<\/p>\n\n\n\n
\u7c21\u5358\u306b\u3059\u308b\u305f\u3081\u3001\u4e00\u8fba$a$\u306e\u7acb\u65b9\u4f53\u3067\u8003\u3048\u3066\u307f\u307e\u3059\u3002<\/p>\n
\u7bb1\u5185\u306e\u5206\u5b50\u306ex\u65b9\u5411\u306e\u30a8\u30cd\u30eb\u30ae\u30fc$\\epsilon_x$\u306f\u3001\u4e95\u6238\u578b\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u3092\u60f3\u5b9a\u3057\u3066\u30b7\u30e5\u30ec\u30c7\u30a3\u30f3\u30ac\u30fc\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3068\u3001<\/p>\n
$$\\epsilon_x=\\frac{{n_x}^2h^2}{8ma^2}$$<\/p>\n
$$n_x=1,2,3,\\cdots$$<\/p>\n
$$h:\u30d7\u30e9\u30f3\u30af\u5b9a\u6570\u3001m:\u5206\u5b50\u306e\u8cea\u91cf$$<\/p>\n
y\u65b9\u5411\u3001z\u65b9\u5411\u3082\u540c\u7b49\u306a\u306e\u3067\u3001\u30a8\u30cd\u30eb\u30ae\u30fc\u6e96\u4f4d$\\epsilon$\u306f\u3001<\/p>\n
$$\\epsilon=({n_x}^2+{n_y}^2+{n_z}^2)\\frac{h^2}{8ma^2}$$<\/p>\n
\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n
\u5206\u5b50\u304c\u3053\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u6e96\u4f4d\u306b\u5206\u914d\u3055\u308c\u308b\u3068\u3057\u3066\u3001\u5206\u914d\u95a2\u6570$q$\u3092\u6c42\u3081\u307e\u3059\u3002<\/p>\n
$$q=\\sum_{i}g_ie^{-(\\epsilon_i-\\epsilon_0)\/kT}$$<\/p>\n
$g_i$\u306f\u5206\u5b50$i$\u306e\u7e2e\u9000\u5ea6\u3001$\\epsilon_i$\u306f$i$\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u3001$\\epsilon_i$\u306f\u57fa\u5e95\u72b6\u614b\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u3067\u3059\u3002<\/p>\n
\u6e29\u5ea6\u304c\u5145\u5206\u9ad8\u3044\u3068\u3057\u3066\u3001\u7e2e\u9000\u3092\u7121\u8996\u3001\u57fa\u5e95\u72b6\u614b\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u30920\u3068\u3059\u308c\u3070<\/p>\n
$$q=\\sum_{i}e^{-\\epsilon_i\/kT}=\\sum_{i,j,k}e^{-({n_x}^2+{n_y}^2+{n_z}^2)h^2\/8ma^2kT}$$<\/p>\n
$$=\\sum_{i}e^{-{n_x}^2h^2\/8ma^2kT}\\sum_{j}e^{-{n_y}^2h^2\/8ma^2kT}\\sum_{k}e^{-{n_z}^2h^2\/8ma^2kT}$$<\/p>\n
$$q_xq_yq_z$$<\/p>\n
\u3053\u3053\u3067\u3001\u548c\u3092\u7a4d\u5206\u306b\u7f6e\u304d\u63db\u3048\u308b\u3068<\/p>\n
$$qx=\\int_0^{\\infty} e^{-{n_x}^2h^2\/8ma^2kT}dn_x=\\frac{\\sqrt{2\\pi ma^2kT}}{h}$$<\/p>\n
\u3088\u3063\u3066<\/p>\n
$$q_x=q_y=q_z=\\frac{\\sqrt{2\\pi ma^2kT}}{h}$$<\/p>\n
$$q=q_xq_yq_z=\\left(\\frac{2\\pi ma^2kT}{h^2}\\right)^{3\/2}$$<\/p>\n
\u3053\u3053\u3067$a^3$\u3092\u4f53\u7a4d$V$\u3068\u8868\u305b\u3070<\/p>\n
$$q=\\left(\\frac{2\\pi mkT}{h^2}\\right)^{3\/2}V$$<\/p>\n
\u5206\u914d\u95a2\u6570\u304c\u6c42\u307e\u3063\u305f\u306e\u3067\u3053\u306e\u5148\u306f\u53e4\u5178\u7d71\u8a08\u529b\u5b66\u3067\u306e\u5c0e\u51fa\u3068\u540c\u3058\u3088\u3046\u306b\u3057\u3066\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n
\u4e00\u4f8b\u3092\u793a\u3057\u3066\u304a\u304d\u307e\u3059\u3002<\/p>\n
\u5206\u5b50\u6570\u3092$N$\u3068\u3059\u308b\u3068\u3001\u30d8\u30eb\u30e0\u30db\u30eb\u30c4\u306e\u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc$F$\u306f<\/p>\n
$$F=-kT\\ln\\frac{q}{N}=-kT\\ln \\Bigr\\{\\left(\\frac{2\\pi mkT}{h^2}\\right)^{3\/2}\\frac{V}{N}\\Bigr\\}$$<\/p>\n
$F=E-TS$\u3088\u308a<\/p>\n
$$S=\\frac{E}{T}+k\\ln \\Bigr\\{\\left(\\frac{2\\pi mkT}{h^2}\\right)^{3\/2}\\frac{V}{N}\\Bigr\\}$$<\/p>\n
\u5b9a\u5727\u6bd4\u71b1\u3092$\\dfrac{5Nk}{2}$\u3068\u3059\u308b\u3068\u3001$E=\\dfrac{5NkT}{2}$\u3088\u308a\u3001<\/p>\n
$$S=\\frac{5}{2}Nk+k\\ln \\Bigr\\{\\left(\\frac{2\\pi mkT}{h^2}\\right)^{3\/2}\\frac{V}{N}\\Bigr\\}$$<\/p>\n
\u4ee5\u4e0a\u3001\u30b6\u30c3\u30af\u30fc\u30eb\u30fb\u30c6\u30c8\u30ed\u30fc\u30c7\u65b9\u7a0b\u5f0f\u304c\u5c0e\u304b\u308c\u305f\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
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