Tianjin University Practice Test (1), Question 20
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This post was last edited by linmuxh on 2015-8-3 at 13:21. 20. If air undergoes adiabatic throttling expansion, dropping from 2100 kPa to 100 kPa without any work being done, and if heat transfer as well as changes in potential and kinetic energy can be ignored, with the ambient temperature T0 = 298.15 K and assuming that air is an ideal gas, then the work loss generated in this process is ( ). A. WL=0 B. WL=25.31 kJ/kmol C. WL=7.55×103 kJ/kmol D. WL=21.0 kJ/kmol
Was a condition missed? There is no amount of substance, nor any volume. Waiting for experts to give guidance
It is equivalent to an isothermal reversible process of an ideal gas! Using 1 kmol as the basis: WL = –f PdV = –f nRT/V; dV = nRT*Ln(V2/V1) = nRT*Ln(P1/P2) = 1*8.314*298.15*Ln(2/1) = 7.55*10^3 KJ/kmol; therefore, the correct answer is (C). It’s quite simple! To solve this problem, one needs to have certain analytical skills and a solid foundation of knowledge! Work hard right away!
This problem indeed lacks necessary conditions; otherwise, it cannot be solved. During adiabatic throttling expansion of an ideal gas, the pressure must decrease and the volume must increase; however, the temperature can change in various ways. Therefore, its molar entropy change is given by △S = Cpm*Ln(T2/T1) + R*Ln(P1/P2). An additional condition must be imposed: throttling expansion results in no change in temperature. Thus, △S = R*Ln(P1/P2) = 8.314*Ln(2100/100) = 25.31 J/K. The work lost, WL, is equal to T0*△S = 7.55*10^3 KJ/kmol.
Because of this question, I went back and reviewed the textbook; actually, the question didn’t lack any conditions. According to the first law of thermodynamics, △U = Q + W = 0; since △U is a function of temperature, it follows that △T = 0.
The original poster is right! Everyone must be careful – the questions themselves are never wrong; some seemingly missing conditions are actually contained within the question itself, and it’s necessary to use one’s solid foundational knowledge to identify them. Such questions invisibly increase the difficulty level!