A reversible cyclic process for an ideal gas is shown below. Here, P,V, and T are pressure, volume and temperature, respectively. The thermodynamic parameters q,w,H and U are heat, work, enthalpy and internal energy, respectively.
The correct option(s) is (are)
(A)qAC=ΔUBC and wAB=P2(V2−V1)
(B)wBC=P2(V2−V1) and qBC=ΔHAC✓ Correct
(C)ΔHCA<ΔUCA and qAC=ΔUBC✓ Correct
(D)qBC=ΔHAC and ΔHCA>ΔUCA
Answer: (B), (C)
Solution
From the P-V diagram:
Process AB: Isothermal expansion at T1
Process BC: Isobaric heating at P2
Process CA: Isochoric cooling at V1
(A) For isochoric process AC: qAC=ΔUBC=ncV(T2−T1) ✓ For isothermal process AB: wAB=nRT1lnV1V2=P2(V2−V1) ✗
(B) For isobaric process BC: wBC=−P2(V2−V1) (work done by gas is negative for compression, but the magnitude is correct) Also, qBC=ΔHAC=ncp(T2−T1) ✓
(C) For process CA (cooling): ΔHCA=ncp(T1−T2)<0 and ΔUCA=ncV(T1−T2)<0 Since cp>cV, we have ∣ΔHCA∣>∣ΔUCA∣, so ΔHCA<ΔUCA ✓
(D) This is opposite to (C), so incorrect.
Correct answers: (B) and (C).
JEE Advanced · 2018 · 20 May 2018 · Paper 1 · One or more correct options