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Explanation & Answer
A--->B: Q = W = integrate PdV = nRT/V dV = nRT ln (VB/VA) = 3RT ln(PA/PB)= 3RTln6
PV = 3RT
T = PV/3R = 100*1000*0.009/(3*8.31) = 36.1 K
Q=W = 3RTln6 = 1612.5J
T does not change so deltaU=0
B-->C
Tc = Vc/VB TB = VA/VB TB = 1/6 TB = 6.02K
Q = 3*3/2R*(6.02-36.1) = -1121.9 J
W = PdeltaV = 100*1000*(0.0015-0.009) = -750J
deltaU = Q-W =-1121.9+750 = 371.9J
C-->A:
Q = Q = 3*3/2R*(36.02-6.02) = 1121.9 J
W= PdeltaV = 0
deltaU = 1121.9 J
efficiency = (WAB+WBC)/QAB = (1612.5-750)/1612.5=53.5%
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