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½¾µ±Ìy[WÅÍAzCÌÌ½ðOñÉµÄ¢Ü·D ntàÌ½ÍAn¿ªntÆ¢¤Àçê½óÔÌÅN±é½Å éÆl¦é±ÆªÅ«Ü·D

Ü¸AMÍwæ1@¥ÍAÈºÌ®ÉÜÆßçêÜ·D
dU = dQ - PdV
±±ÅAdU ÍnÌàGlM[AT Í·xiâÎ·xjAP Í³ÍAV ÍÌÏÅ·D nÆÍ©Ä¢éWcÆ»êªüÁ½ ð\µÜ·D ±±Å¾¤WcÆÍà¿ëñªqÌWcÅ èA½ÉÖ^µ¾éªqðSÄ ÉüêÄ±êðnÆÄÑÜ·D i½¾µA ª½ÅÅ«Ä¢é©HÍl¦È¢Rgcj ÅA±Ì®Í½ð¾ÁÄ¢é©Æ¢¤ÆA»ÌªqWcªàï·éGlM[ÍMÉæÁÄÁµAªqWcªdð·é±ÆÅ¸·éÆ¢¤±ÆÅ·D ½¾»ê¾¯ÌRgÅ·D ½¾µAdÆÍ±±ÅÍ çPdV Å·©çËD Z¨ÜÅÍKµÜ¹ñæD

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dS = dQ/T
ÆAGgs[ÌTOªoÄ«Ü·D

2ÂÌ®©çAÂ½nÉ¨¯éMÍwî{ûö®ÆÄÎêéA
dU = TdS - PdV
ª±©êÜ·D Â½nÆÍAªqWÌÉoüèªÈ¢Æ«Aá¦Îæ»©ç¢GlM[ðÁ½ªqªüÁÄ«ÄàGlM[ªÁµ½AÈñÄ±ÆÌÈ¢óÔð¼èµÄ¢Ü·D

»w½ðµ¤Æ«AêÊÉ³Í§äÍs¢Ü¹ñ©çA±±ÅÍè³Â«ºÉÂ¢Äl¦ÄÝÜµå¤D éóÔ1©çdQÌMð¾ÄóÔ2ÉÈÁ½Æ·éÆA
dU ( = U₂ - U₁ ) = Q - P(V₂ - V₁ )
µ½ªÁÄA
Q = (U₂ + PV₂ ) - (U₂ + PV₂)
Å·D±Ì U + PV ÍÇoÄéÌÅAG^s[ H ÆµÄA
H = U + PV
Éæè\³êÜ·D G^s[ÍAnÌÂMÆdÌÊÅ·D

³ÄA é½ªN«é©Ç¤©ÉÂ¢Äl¦ÄÝÜµå¤D à¤êxMÍwæ2@¥©çNEWEXÌs®ðl¦éÆA
dS dQ/T
Å·Dî{ûö®©çA½tóÔÉ¨¢ÄÍ
dU + PdV - TdS = 0
ª¾çêÜ·D ·Èí¿AÌÏÆGgs[ªêèÅ êÎÂt½É¨¢ÄàGlM[Ï»ÊÍ 0 Å éA ÂÜèAàGlM[ÍiÅ¬ÌjêèlðÆé±Æð¦µÄ¢Ü·D
è³Eè·ºÅÍA
d(U + P - TS) = 0
Å·D±±ÅAMuXGlM[ G ðA
G = U + PV - TS = H - TS
Éæèè`·éÆA½tóÔÉ¨¢ÄÍ
dG = 0
Ü½ANEWEXÌs®ÜÅßéÆA©IÏ»É¨¢Ä
dG < 0
ª¾çêÜ·D

MÍwæ1@¥ÍAMI½tóÔÉÂ¢Äl¦Ä¢Üµ½D µ©µAæ2@¥ð±ü·é±ÆÅAnÌóÔÏ»ÉÍûüª é±Æª¦³ê½í¯Å·D

È¨A±±ÅÍdvÈà¤1ÂÌ¨ÊÅ éAwzcGlM[ A ÉÂ¢ÄÍÈªµÜµ½D wzcGlM[ÍAèÏÏ»É¨¯éMuXGlM[É·éàÌÅ·D ÅÉq×½æ¤ÉAntà½ÍtÌÆ¢¤èÏÌnàÉ¨¯é½Å·ÌÅAàGlM[ÌãíèÉ HA©RGlM[MuXGlM[ÅÈ A ðp¢Äc_µÄàÙÆñÇlÍÏíçÈ¢Æ¾¦éÅµå¤DiG = H - TS ÌãíèÉA A = U - TSj

÷¬ÈÂtÏ»É¨¯éMuXGlM[ G ÌÏ»Ê dG ÉÎµÄAG = U + PV - TS æèA
dG = dU + PdV + VdP - TdS - SdT
ª¾çêÜ·D ±êÉMÍwî{ûö®ðãü·éÆA
dG = VdP - SdT
ÆÈèÜ·D
êûAè·Eá³»É¨¯é G ÌS÷ªÍ
dG = (ÝG/ÝP)_T + (ÝG/ÝT)_P
Å·ÌÅAär·éÆA
(ÝG/ÝP)_T = V, -(ÝG/ÝT)_P = S
ª¾çêÜ·D ½¾©éx³ê½æ¤ÈCªµÈàÈ¢©àµêÜ¹ñªAOÒÍ÷¬ÈÏ»ÉÎ·éÏ»ÊAãÒÍwIÈS÷ªÅ é±ÆÉCðt¯Äº³¢D

(ÝG/ÝP)_T = V ðÏª·éÆA
çdG = çVdP
ª¾çêÜ·D ±±ÅAPV = RT æè V = RT/P ðãüµÄA
çdG = RTçdP/P
ÆÈèÜ·D WóÔÉ¨¯éMuXGlM[ð GßA³Íð Pß Æ·éÆA
G - Gß = RTln(P/Pß)
ª¾çêÜ·D
MuXGlM[ª³ÍÉË¶·élÅ éÆ¢¤ÌÍðµâ·¢Æv¢Ü·D

±±©çæ¤âA»wÌbÉüèÜ·D Ç¤¢¤±Æ©Æ¢¤ÆA»w½ÉæÁÄnÌ±qªÏ»·éA·Èí¿»w½ªN±éêðl¦Ü·D ÅàÜ¾ACÌÌbÅäµÄ¾³¢D ±±ÜÅêÎntÖÌWJÍà¤µÅ·©çD

»wÏ»ªN±énÉ¨¢ÄÍAMuXGlM[ÌS÷ªÍA¬ª i Ì±qÌ n(i) ðp¢ÄA
dG = (ÝG/ÝT)_P,n(i) + (ÝG/ÝP)_T,n(i) + °_i{ÝG/Ýn(i)}_P,n(ji)
Æ«\¹Ü·D Y¦Ì n(ji) Íui ÈOÌ¬ª j Ì±qÌ n(j) ªêèÉÛ½êÄ¢év±Æð\µÜ·D ±±ÅA±Ì±Öð
Ê_i = {ÝG/Ýn(i)}_P,n(ji)
Æ¨ÆA
dG = -SdT + VdP + °Ê_idn(i)
ª¾çêÜ·D ±Ì Ê_i ðA¬ª i Ì»w|eVÆÄÑÜ·D e¬ªªÆ§É¶ÝµÄ¢éÌÅ êÎA¬ª i Ì»w|eVÍ¬ª i Ìª³ P_i ðp¢ÄA
Ê_i = Êß + RT ln(P_i/Pß)
Å\³êÜ·D

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Æ±ëÅACÌ¬ª i Ìª¦ð y_i Å\·ÆAy_i = P_i/Pß ÈÌÅA
Ê_i = Êß + RT ln y_i
ÆÈèA¾ñ¾ñÇÝé® Ê = Êß + RT ln C Éßt¢Ä«Üµ½ËD

ªq A Æ B ªÏ··éæ¤È»w½tA = Bðl¦Ü·D è·Eè³ºÅÍA
dG = °Ê_idn(i)
Å·ËD ½tªEÉiÞÆ«Adn(B) = -dn(A) Å·©çAdG ÍA
dG = (Ê_Bß + RT ln y_B) - (Ê_Aß + RT ln y_A)
Æ±ÆªÅ«Ü·D
±±ÅA½tóÔÉ¨¢ÄÍdG = 0Å·©çA
Ê_Aß + RT ln y_A = Ê_Bß + RT ln y_B
ª¾çêÜ·D

êÊÉA»w½ta A + b B + ... = m M + n N + ...ia, b, m, n, ...Í»wÊ_WjÉ¨¢ÄA
a(Ê_Aß + RT ln y_A) + b(Ê_Bß + RT ln y_B) + ... = m(Ê_Mß + RT ln y_M) + n(Ê_Nß + RT ln y_N) ...
ª¬è§¿Ü·D
±Ì®ðÏ`·éÆA
(y_M^m y_Nⁿ ...)/(y_A^a y_B^b ...) = exp[ { (a Ê_Aß + b Ê_Bß + ...) - (m Ê_Mß + n Ê_Nß ...) } / RT ]
ª¾çêÜ·D ±Ì¶ÓÍÇ±©Å©½±Æª èÜ·Ëc»¤A½tèÅ·D EÓÌÏÍÍ½ÍSÄêèÅ·ÌÅAEÓÍèÅ·D ±êð K Æ¨ÆA±Ì½Ì½tè K ªA
K = (y_M^m y_Nⁿ ...)/(y_A^a y_B^b ...)
ÆµÄ¾çêéÌÅ·D

êûA±Ì½OãÌW»w|eVÌaðWMuXGlM[Ï»ÆÄÑA
¢Gß = (m Ê_Mß + n Ê_Nß ...) - (a Ê_Aß + b Ê_Bß + ...)
Æè`³êÜ·D MuXGlM[àAâÎlÍª©çÈÄàA»ÌGlM[Ï»ÍdvÈÊÅ·D ãÌ®©çAMuXGlM[ÌÏ»ÍA
¢G = -RT ln K
Å é±Æªª©èÜ·ËD ÊíÍ½èÉ·ZµAa Ì A + b Ì B + ... ©ç m Ì M + n Ì N ª¶¬·é½É¨¯éMuXGlM[Ï»ðA½èÉ·Zµ kJ/mol PÊÅ\µÜ·D

±Ì®©çA½ÌMuXGlM[Ï»ÉÖ·é¢Â©ÌdvÈ«¿ª±©êÜ·D á¦ÎAãÌ½tÉÎ·éMuXGlM[Ï» ¢G₁ ÉÎµAÊÌ»w½ta A + b B + ... = x X + y Y + ...ÉÎ·éMuXGlM[Ï»ð ¢G₂ Å éÆµÜ·D àµA¢G₂ ª ¢G₁ æè 5.7 kJ/mol ¬³¢ÈçÎAx X + y Y + ... Í a A + b B + ... Éä× 10 {½¶¬µâ·¢i½tèª10{jÆ¢¤±Æªª©èÜ·D Ü½A»w½tm M + n N + ... = x X + y Y + ...ÌMuXGlM[Ï»ª ¢G₂ - ¢G₁ Å éÆ¢¤±ÆªA½Æ¦¼ÚèÅ«È©Á½ÆµÄàª©éÌÅ·D

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