{"id":399,"date":"2023-12-03T23:13:34","date_gmt":"2023-12-03T23:13:34","guid":{"rendered":"https:\/\/tbits.jp\/plus\/?p=399"},"modified":"2023-12-03T23:13:36","modified_gmt":"2023-12-03T23:13:36","slug":"raoult-vanthoff","status":"publish","type":"post","link":"https:\/\/tbits.jp\/plus\/raoult-vanthoff\/","title":{"rendered":"\u30e9\u30a6\u30fc\u30eb\u306e\u6cd5\u5247\u304b\u3089\u30d5\u30a1\u30f3\u30c8\u30db\u30c3\u30d5\u306e\u5f0f\u306e\u5c0e\u51fa"},"content":{"rendered":"\n

\u30e1\u30a4\u30f3\u30b5\u30a4\u30c8\u306e\u8a18\u4e8b\u300c\u6d78\u900f\u5727\u3068\u306f\u4f55\u304b\uff1f\u3000\u308f\u304b\u308a\u3084\u3059\u304f\u8aac\u660e\u3057\u3066\u307f\u305f<\/a>\u300d\u306e\u4e2d\u3067\u6c34\u3068\u6eb6\u6db2\u306e\u84b8\u6c17\u5727\u3068\u6d78\u900f\u5727\u306e\u95a2\u4fc2\u306b\u3064\u3044\u3066\u3075\u308c\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

\u3053\u3053\u3067\u306f\u305d\u306e\u95a2\u4fc2\u3092\u5f0f\u3092\u7528\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\u3053\u3068\u306e\u767a\u7aef<\/h2>\n\n\n\n

Q\uff06A\u30b5\u30a4\u30c8\u3067\u300c\u6d78\u900f\u5727\u3068\u98fd\u548c\u84b8\u6c17\u5727\u306e\u95a2\u4fc2\u306b\u3064\u3044\u3066\u8cea\u554f\u3067\u3059\u3002\u300d<\/a>\u3068\u3044\u3046\u8cea\u554f\u3092\u898b\u3064\u3051\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

\n

U\u5b57\u7ba1\u306e\u4e2d\u306b\u6eb6\u6db2\u3068\u6c34\u304c\u5165\u3063\u3066\u3044\u3066\u534a\u900f\u819c\u3067\u4ed5\u5207\u3089\u308c\u3066\u3044\u308b\u72b6\u614b\u3067\u306f(\u6c34\u306e\u307f\u304c\u901a\u308b\u3053\u3068\u304c\u3067\u304d\u308b)\u3001\u6d78\u900f\u5727\u306b\u3088\u3063\u3066\u5f53\u7136\u6db2\u9762\u5dee\u304c\u751f\u3058\u307e\u3059\u3002\u305d\u308c\u3092\u30e9\u30a6\u30fc\u30eb\u306e\u6cd5\u5247\u306b\u3088\u308b\u98fd\u548c\u84b8\u6c17\u5727\u306e\u5dee\u306b\u7740\u76ee\u3057\u3066\u8aac\u660e\u3057\u3088\u3046\u3068\u3057\u305f\u306e\u3067\u3059\u304c\u3088\u304f\u308f\u304b\u3089\u306a\u304f\u306a\u3063\u3066\u304d\u307e\u3057\u305f\u3002 \uff1c\u7565\uff1e<\/p>\n<\/blockquote>\n\n\n\n

\u6eb6\u6db2\u306e\u6d78\u900f\u5727\u3068\u84b8\u6c17\u5727\u306b\u95a2\u4fc2\u304c\u3042\u308b\u306e\u304b\uff1f\u3000\u3068\u3044\u3046\u8cea\u554f\u3067\u3059\u3002<\/p>\n\n\n\n

\u56de\u7b54\u306e\u5168\u3066\u304c\u300c\u84b8\u6c17\u5727\u3068\u6d78\u900f\u5727\u306f\u5168\u304f\u5225\u306e\u7279\u6027\u306a\u306e\u3067\u95a2\u4fc2\u306a\u3044<\/strong>\u300d\u3068\u3044\u3046\u3082\u306e\u3067\u3001\u8cea\u554f\u8005\u3082\u305d\u306e\u56de\u7b54\u306b\u7d0d\u5f97\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

\u3067\u3082\u58f0\u3092\u5927\u306b\u3057\u3066\u8a00\u3044\u305f\u3044\u306e\u3067\u3059\u3002<\/p>\n\n\n\n

\u300c\u84b8\u6c17\u5727\u3068\u6d78\u900f\u5727\u306b\u95a2\u4fc2\u304c\u306a\u3044\u308f\u3051\u304c\u306a\u3044<\/span><\/strong>\u300d<\/p>\n\n\n\n

\u305d\u3053\u3067\u3001\u304a\u305d\u3089\u304f\u3053\u306e\u8cea\u554f\u8005\u304c\u6c42\u3081\u3066\u3044\u308b\u3067\u3042\u308d\u3046\u56de\u7b54\u3092\u793a\u3057\u305f\u3044\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

\u30e9\u30a6\u30fc\u30eb\u306e\u6cd5\u5247\u3068\u30d5\u30a1\u30f3\u30c8\u30db\u30c3\u30d5\u306e\u5f0f<\/h2>\n\n\n\n

\u307e\u305a\u306f\u6eb6\u6db2\u306e\u84b8\u6c17\u5727\u964d\u4e0b\u3092\u8868\u3059\u30e9\u30a6\u30fc\u30eb\u306e\u6cd5\u5247\u3068\u6d78\u900f\u5727\u3092\u8868\u3059\u30d5\u30a1\u30f3\u30c8\u30db\u30c3\u30d5\u306e\u5f0f\u3092\u307f\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

\u30e9\u30a6\u30fc\u30eb\u306e\u6cd5\u5247<\/strong>
$$Ps=Pw\\chi \u3000 (1)$$
$$\\chi=\\frac{nw}{nw+ns}\u3000(2)$$<\/p>\n\n\n\n

$Ps$:\u6eb6\u6db2\u306e\u6c34\u84b8\u6c17\u5727\u3001$Pw$:\u6c34\u306e\u6c34\u84b8\u6c17\u5727\u3001$\\chi$:\u6eb6\u6db2\u4e2d\u306e\u6c34\u306e\u30e2\u30eb\u5206\u7387\u3001$n_w$:\u6eb6\u6db2\u4e2d\u306e\u6c34\u306e\u30e2\u30eb\u6570\u3001$n_s$:\u6eb6\u6db2\u4e2d\u306e\u6eb6\u8cea\u306e\u30e2\u30eb\u6570_<\/p>\n\n\n\n

\u30d5\u30a1\u30f3\u30c8\u30db\u30c3\u30d5\u306e\u5f0f<\/strong>
$$\\pi V=n_sRT \u3000 (3)$$<\/p>\n\n\n\n

$\\pi$\uff1a\u6d78\u900f\u5727\u3001$V$\uff1a\u6eb6\u6db2\u306e\u4f53\u7a4d\u3001$n_s$\uff1a\u6eb6\u8cea\u306e\u30e2\u30eb\u6570\u3001$R$\uff1a\u6c17\u4f53\u5b9a\u6570\u3001$T$\uff1a\u6e29\u5ea6<\/p>\n\n\n\n

\u30e9\u30a6\u30fc\u30eb\u306e\u6cd5\u5247\u304b\u3089\u30d5\u30a1\u30f3\u30c8\u30db\u30c3\u30d5\u306e\u5f0f\u3092\u5c0e\u3051\u3070\u76ee\u6a19\u9054\u6210\u3067\u3059\u3002\u3068\u3082\u306b\u5e0c\u8584\u6eb6\u6db2\u3067\u6210\u308a\u7acb\u3064\u8fd1\u4f3c\u5f0f\u306b\u904e\u304e\u307e\u305b\u3093\u304b\u3089\u3001\u8fd1\u4f3c\u7684\u306b\u4e00\u81f4\u3059\u308b\u3053\u3068\u3092\u793a\u305b\u3070\u3044\u3044\u3067\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

\u6fc3\u5ea6\u306e\u8868\u3057\u65b9\u304c\u9055\u3046\u306e\u3067\u305d\u3053\u304c\u9762\u5012\u3067\u3059\u3002<\/p>\n\n\n\n

\u8003\u3048\u65b9<\/h2>\n\n\n\n
\"\"<\/figure>\n\n\n\n

\u56f3\u306e\u3088\u3046\u306aO\u5b57\u5b98\u306e\u4e2d\u306b\u534a\u900f\u819c\u3092\u306f\u3055\u3093\u3067\u6c34\u3068\u6eb6\u6db2\u3092\u5165\u308c\u307e\u3059\u3002<\/p>\n\n\n\n

\u5145\u5206\u6642\u9593\u304c\u7d4c\u3064\u3068\u5e73\u8861\u72b6\u614b\u306b\u306a\u308b\u306f\u305a\u3067\u3059\u3002\u3053\u306e\u3068\u304d\u6db2\u306f\u5f53\u7136\u6d41\u52d5\u306a\u3069\u305b\u305a\u9759\u6b62\u3057\u3066\u3044\u308b\u306f\u305a\u3067\u3059\u3002\u305d\u3046\u3067\u306a\u3051\u308c\u3070\u6c38\u4e45\u6a5f\u95a2\u3067\u3059\u304b\u3089\u3002<\/p>\n\n\n\n

\u6eb6\u6db2\u3088\u308a\u6c34\u306e\u65b9\u304c\u84b8\u6c17\u5727\u304c\u9ad8\u3044\u3067\u3059\u304c\u3001\u6c34\u304b\u3089\u84b8\u767a\u3057\u305f\u6c34\u84b8\u6c17\u304c\u6eb6\u6db2\u306b\u5438\u53ce\u3055\u308c\u308b\u3088\u3046\u306a\u3053\u3068\u306f\u8d77\u3053\u308a\u307e\u305b\u3093\u3002\u305d\u3046\u3059\u308b\u3068\u6db2\u304c\u6d41\u52d5\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\u3082\u3057\u305d\u3046\u306a\u3089\u5e73\u8861\u72b6\u614b\u3067\u306f\u6c34\u3068\u6eb6\u6db2\u306e\u84b8\u6c17\u5727\u5dee\u306f\u6db2\u9762\u5dee\u3067\u30ad\u30e3\u30f3\u30bb\u30eb\u3055\u308c\u3066\u3044\u308b\u306f\u305a\u3067\u3059\u3002<\/p>\n\n\n\n

\u6db2\u9762\u306b\u63a5\u3059\u308b\u6c17\u76f8\u306e\u6c34\u84b8\u6c17\u5727\u306f\u9ad8\u3055\u306b\u3088\u3063\u3066\u5909\u308f\u308a\u307e\u3059\u3002\u6c34\u306e\u65b9\u304c\u6eb6\u6db2\u3088\u308a\u6db2\u9762\u304c\u4f4e\u3044\u306e\u3067\u3001\u305d\u306e\u5206\u6db2\u9762\u306b\u63a5\u3057\u3066\u3044\u308b\u90e8\u5206\u306e\u6c34\u84b8\u6c17\u304c\u9ad8\u304f\u306a\u3063\u3066\u3044\u308b\u306f\u305a\u3067\u3059\u3002<\/p>\n\n\n\n

\u3053\u308c\u304c\u6c34\u3068\u6eb6\u6db2\u306e\u84b8\u6c17\u5727\u5dee\u3068\u4e00\u81f4\u3059\u308b\u6db2\u9762\u5dee\u3092\u8a08\u7b97\u3057\u3001\u305d\u306e\u6db2\u9762\u5dee\u304c\u751f\u3058\u308b\u6d78\u900f\u5727\u3092\u5c0e\u3044\u3066\u305d\u308c\u304c\u30d5\u30a1\u30f3\u30c8\u30db\u30c3\u30d5\u306e\u5f0f\u306b\u4e00\u81f4\u3059\u308b\u3053\u3068\u3092\u793a\u305b\u3070\u3088\u3044\u3067\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

\u5225\u306bO\u5b57\u7ba1\u306b\u3057\u306a\u304f\u3066\u3082\u5468\u56f2\u306e\u6c34\u84b8\u6c17\u91cf\uff08\u6e7f\u5ea6\uff09\u3068\u6c34\u9762\u304c\u5e73\u8861\u306b\u306a\u3063\u305f\u72b6\u614b\u3092\u8003\u3048\u308c\u3070\u3044\u3044\u306e\u3067\u3059\u304c\u3001\u30a4\u30e1\u30fc\u30b8\u3057\u3084\u3059\u3044\u3068\u601d\u3044O\u5b57\u7ba1\u3092\u4f7f\u3044\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

\u84b8\u6c17\u5727\u5dee\u304c\u30ad\u30e3\u30f3\u30bb\u30eb\u3055\u308c\u308b\u6db2\u9762\u5dee\u306e\u8a08\u7b97<\/h2>\n\n\n\n

\u30fb\u6c34\u3068\u6eb6\u6db2\u306e\u84b8\u6c17\u5727\u5dee\u306e\u8a08\u7b97<\/strong>
\u6c34\u3068\u6eb6\u6db2\u306e\u84b8\u6c17\u5727\u5dee\u3092$\\Delta P$\u3068\u3059\u308b\u3068\u3001\uff08\uff11\uff09\u5f0f\u3088\u308a
$$\\Delta P=Pw-Ps=Pw-Pw\\chi=Pw(1-\\chi) \u3000 (4)$$<\/p>\n\n\n\n

\u30fb\u6db2\u9762\u5dee\u306b\u3088\u308b\u6c34\u84b8\u6c17\u306e\u5727\u529b\u5dee<\/strong>
\u6db2\u9762\u5dee\u3092$\\Delta h$\u3001\u5727\u529b\u5dee\u3092$\\Delta P$\u3068\u3059\u308b\u3068
$$\\Delta P=\\rho g \\Delta h $$
$\\rho$:\u6c34\u84b8\u6c17\u306e\u5bc6\u5ea6\u3001$g$\uff1a\u91cd\u529b\u5b9a\u6570
$$\\Delta h=\\frac{\\Delta P}{\\rho g}$$
(4)\u5f0f\u3092\u4ee3\u5165\u3057\u3066
$$ \\Delta h=\\frac{Pw(1-\\chi)}{\\rho g} \u3000(5)$$
\u6c34\u84b8\u6c17\u306e\u5bc6\u5ea6$\\rho$\u306f\u3001\u6c34\u84b8\u6c17\u306e\u4f53\u7a4d$V\u2019$\u3000\u4f53\u7a4d$V\u2019$\u306e\u6c34\u84b8\u6c17\u306e\u8cea\u91cf\u3092$M$
$$ \\rho=\\frac{M}{V\u2019}$$
\u6c34\u306e\u5206\u5b50\u91cf\u3092$m$\u3001\u4f53\u7a4d$V\u2019$\u306e\u6c34\u84b8\u6c17\u306e\u30e2\u30eb\u6570$n\u2019$\u3068\u3059\u308b\u3068$M=mn\u2019$\u3088\u308a
\u7406\u60f3\u6c17\u4f53\u306e\u72b6\u614b\u65b9\u7a0b\u5f0f$PV=\uff4eRT$\u3088\u308a\u3001
$$\\frac{n\u2019}{V\u2019}= \\frac{P\u2019}{RT}$$
$$\\rho=\\frac{mn\u2019}{V\u2019}=\\frac{mP\u2019}{RT}$$
\u3053\u3053\u3067\u3001\u6c34\u84b8\u6c17\u306e\u5727\u529b$P\u2019$\u306f\u3001\u9ad8\u3055\u306b\u3088\u3063\u3066\u7570\u306a\u308b\u304c\u3001\u305d\u306e\u5dee\u306f\u5c0f\u3055\u3044\u305f\u3081\u3001\u6c34\u306e\u84b8\u6c17\u5727$Pw$\u3068\u7b49\u3057\u3044\u3068\u304a\u304f\u3068\u3001
$$\\rho=\\frac{mP\u2019}{RT}=\\frac{mPw}{RT}$$
(5)\u5f0f\u306b\u4ee3\u5165\u3059\u308b\u3068
$$\\Delta h=\\frac{Pw(1-\\chi)}{\\rho g}=\\frac{RT(1-\\chi)}{mg} \u3000 (6)$$<\/p>\n\n\n\n

\u6db2\u9762\u5dee$\\Delta h$\u304c\u6c42\u307e\u308a\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

\u6c42\u3081\u305f\u6db2\u9762\u5dee\u3092\u751f\u3058\u3055\u305b\u308b\u6d78\u900f\u5727\u306e\u8a08\u7b97<\/h2>\n\n\n\n

\u6db2\u9762\u5dee$\\Delta h$\u306b\u3088\u3063\u3066\u751f\u3058\u308b\u5727\u529b\u5dee\u3092$\\pi$\u3068\u3059\u308b\u3068<\/p>\n\n\n\n

$$\\pi =\\rho g \\Delta h $$<\/p>\n\n\n\n

$\\Delta h$\u306b(6)\u5f0f\u3092\u4ee3\u5165\u3059\u308b\u3068
$$\\pi =\\rho g \\frac{RT(1-\\chi)}{mg}=\\rho \\frac{RT(1-\\chi)}{m}\u3000 (7)$$
\u3053\u3053\u3067\u3001\u6eb6\u6db2\u306e\u6fc3\u5ea6\u304c\u5145\u5206\u4f4e\u304f\u3001\u6eb6\u6db2\u306e\u5bc6\u5ea6\u306f\u6c34\u306e\u5bc6\u5ea6\u306b\u7b49\u3057\u3044\u3068\u3057\u3001\u6eb6\u6db2\u306e\u4f53\u7a4d\u3092$V$\u3001\u4f53\u7a4d$V$\u306e\u6c34\u306e\u30e2\u30eb\u6570\u3092$n_w$\u3001\u6c34\u306e\u5206\u5b50\u91cf\u3092$m$\u3068\u3059\u308b\u3068
$$\\rho=\\frac{mn_w}{V}$$
(7)\u5f0f\u306b\u4ee3\u5165\u3057\u3066
$$\\pi =\\frac{mn_wRT(1-\\chi)}{mV} =\\frac{n_wRT(1-\\chi)}{V}$$
$$\\chi=\\frac{n_w}{n_w+n_s}$$\u3088\u308a\u3001
$$1-\\chi=\\frac{n_s}{n_w+ns}$$
\u3088\u3063\u3066\u3001
$$\\pi =\\frac{nwRTns}{V(n_w+n_s)}$$
\u6eb6\u6db2\u306e\u6fc3\u5ea6\u304c\u8584\u3044\u5834\u5408\u3001
$$\\frac{nw}{(n_w+n_s)}\\simeq 1 $$
\u3088\u3063\u3066\u3001
$$\\pi =\\frac{RTn_s}{V}$$
$$\\pi V=n_sRT $$<\/p>\n\n\n\n

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