[問題]熱力學求entropy

看板Chemistry作者時間10年前 (2014/02/11 14:45), 編輯推噓3(3推 0噓 21→)
留言24則, 2人參與, 最新討論串1/2 (看更多)
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 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 42.70.229.209 ※ 編輯: littlechili 來自: 42.70.229.209 (02/11 15:03)
推
02/13 20:36, , 1F
entropy is state function
02/13 20:36, 1F
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02/13 20:36, , 2F
所以不管是否可逆過程 △S=S2-S1
02/13 20:36, 2F
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02/13 20:37, , 3F
system:the real gas
02/13 20:37, 3F
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02/13 20:37, , 4F
重自由度來看F=C-P+2=1-1+2=2
02/13 20:37, 4F
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02/13 20:37, , 5F
故可另S=S(V,T)描述
02/13 20:37, 5F
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02/13 20:37, , 6F
dS=(∂S/∂T)v*dT+(∂S/∂V)T*dV
02/13 20:37, 6F
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02/13 20:37, , 7F
(∂S/∂T)v=Cv/T & (∂S/∂V)T=(∂P/∂T)v
02/13 20:37, 7F
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02/13 20:37, , 8F
dS=Cv/T*dT+(∂P/∂T)v*dV
02/13 20:37, 8F
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02/13 20:38, , 9F
代入eq'n of state & constant Cv
02/13 20:38, 9F
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02/13 20:38, , 10F
積分得到△Ssys (1)(2)(3)(4)都是把狀態帶入△Ssys
02/13 20:38, 10F
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02/13 20:38, , 11F
接下來計算△S(surr)
02/13 20:38, 11F
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02/13 20:39, , 12F
(1)△Ssurr=Qsurr./T
02/13 20:39, 12F
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02/13 20:39, , 13F
且Qsurr.=-Qsys
02/13 20:39, 13F
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02/13 20:39, , 14F
by 1st law △Usys=Qsys+Wsys
02/13 20:39, 14F
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02/13 20:39, , 15F
isothermal & ideal gas & free expansion
02/13 20:39, 15F
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02/13 20:39, , 16F
Qsys=0 △Ssurr=0
02/13 20:39, 16F
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02/13 20:39, , 17F
(2)by 1st law Qsys=-Wsys
02/13 20:39, 17F
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02/13 20:39, , 18F
eq'n of state帶入Wsys=-∫pdv/T
02/13 20:39, 18F
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02/13 20:40, , 19F
△Ssurr=Wsys/T
02/13 20:40, 19F
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02/13 20:40, , 20F
對於(3)(4)adiabatic process
02/13 20:40, 20F
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02/13 20:41, , 21F
Qsurr.=0 △Ssurr=0
02/13 20:41, 21F
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02/13 20:41, , 22F
△Stotal=△Ssys.+△Ssurr.即可算出(1)(2)(3)(4)
02/13 20:41, 22F
推
02/13 20:43, , 23F
(4)△Ssys修改一下 isentropic process △Ssys=0
02/13 20:43, 23F
推
02/13 21:44, , 24F
1的自由膨脹沒有entropy變化?
02/13 21:44, 24F
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文章代碼(AID): #1I-SST-G (Chemistry)
‣ 更多 littlechili 的文章
文章代碼(AID): #1I-SST-G (Chemistry)