102A Midterm 2

# 102A Midterm 2 - Problem#1(10 points For ideal gas PV=RT...

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Problem #1 (10 points) For ideal gas, PV =RT Problem #2 (30 points) (1)T f =T i (P f /P i ) R/Cp T i =298K, P i =650bar, P f =1bar, Cp =29.3J/(mol K) So T f =47.4K (2)W=N(U f -U i )=NCv(T f -T i )=(P i V i /RT i )Cv(T f -T i ) V i =0.167m 3 , Cv=Cp/Y, or Cv=Cp-R W=23020kJ

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Problem #4 (30 Points) Prove that 2 1 V T T V S α γ κ ⎛⎞ =+ ⎜⎟ ⎝⎠ , where is p V C C is the thermal expansion coefficient, and T is the thermal compressibility. (, ) p P V T S CT T SS STV dT dV TV = ∂∂ () 1 VV V V V U TU T S C TT = ⎛⎞⎛ = ⎜⎟⎜ ⎝⎠⎝ [ Relation] SP Maxwell VT ⎛⎞⎛⎞ = ⎜⎟⎜⎟ ⎝⎠⎝⎠ V V C P ds dT dV 5points {take derivative with respect to temperature at constant pressure} P PV P V P CC S T T TTTTT = + Recall: p P S T = = V VP + 1 p C TPV T T == ++ 5 points (all the previous steps shown were explained in detailed during lecture from problem 6.25) 1 p Vp T PVT PP V T ∂∂∂ =− = 2 11 p pP P V C TP V V V C C VTT C = 10 points
2 22 T 1 11 PP T T

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102A Midterm 2 - Problem#1(10 points For ideal gas PV=RT...

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