ee作者littlechili (littlechili)
看板Chemistry
標題[問題]熱力學求entropy
時間Tue Feb 11 14:45:46 2014
題目:
1mole真實氣體遵守PV=RT+bP之狀態方程式
(1.) 從(T,V1)經等溫自由膨脹到終點(T,V2)，求△Ssys? △Ssurr?與△Stotal?
(2.) 從(T,V1)經等溫可逆膨脹到終點(T,V2)，求△Ssys? △Ssurr?與△Stotal?
(3.) 從(T1,V1,P1)經絕熱自由膨脹到終點(T2,V2,P2) ，求△Ssys? △Ssurr?與△
Stotal?
(4.) 從(T1,V1,P1)經絕熱可逆膨脹到終點(T2,V2,P2) ，求△Ssys? △Ssurr?與△
Stotal?
對於上面四種膨脹程序的entropy求法一直搞不清楚，
煩請高手們幫忙釐清這四種情況的求法(尤其是自由膨脹)
謝謝
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※ 編輯: littlechili 來自: 42.70.229.209 (02/11 15:03)
1F：推 guitarspirit:entropy is state function 02/13 20:36
2F：→ guitarspirit:所以不管是否可逆過程 △S=S2-S1 02/13 20:36
3F：→ guitarspirit:system:the real gas 02/13 20:37
4F：→ guitarspirit:重自由度來看F=C-P+2=1-1+2=2 02/13 20:37
5F：→ guitarspirit:故可另S=S(V,T)描述 02/13 20:37
6F：→ guitarspirit:dS=(∂S/∂T)v*dT+(∂S/∂V)T*dV 02/13 20:37
7F：→ guitarspirit:(∂S/∂T)v=Cv/T & (∂S/∂V)T=(∂P/∂T)v 02/13 20:37
8F：→ guitarspirit:dS=Cv/T*dT+(∂P/∂T)v*dV 02/13 20:37
9F：→ guitarspirit:代入eq'n of state & constant Cv 02/13 20:38
10F：→ guitarspirit:積分得到△Ssys (1)(2)(3)(4)都是把狀態帶入△Ssys 02/13 20:38
11F：→ guitarspirit:接下來計算△S(surr) 02/13 20:38
12F：→ guitarspirit:(1)△Ssurr=Qsurr./T 02/13 20:39
13F：→ guitarspirit:且Qsurr.=-Qsys 02/13 20:39
14F：→ guitarspirit:by 1st law △Usys=Qsys+Wsys 02/13 20:39
15F：→ guitarspirit:isothermal & ideal gas & free expansion 02/13 20:39
16F：→ guitarspirit:Qsys=0 △Ssurr=0 02/13 20:39
17F：→ guitarspirit:(2)by 1st law Qsys=-Wsys 02/13 20:39
18F：→ guitarspirit:eq'n of state帶入Wsys=-∫pdv/T 02/13 20:39
19F：→ guitarspirit:△Ssurr=Wsys/T 02/13 20:40
20F：→ guitarspirit:對於(3)(4)adiabatic process 02/13 20:40
21F：→ guitarspirit:Qsurr.=0 △Ssurr=0 02/13 20:41
22F：→ guitarspirit:△Stotal=△Ssys.+△Ssurr.即可算出(1)(2)(3)(4) 02/13 20:41
23F：推 guitarspirit:(4)△Ssys修改一下 isentropic process △Ssys=0 02/13 20:43
24F：推 o810418:1的自由膨脹沒有entropy變化? 02/13 21:44