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Question:

One mole of an ideal gas in initial state A undergoes a cyclic process ABCA, as shown in Fig. Its pressure at A is P0. Choose the correct option(s) from the following. Internal energies at A and B are the same. Work done by the gas in process AB is P0V0ln4. Pressure at C is P0/4. Temperature at C is T0/4.

Work done by the gas in process AB is P0V0ln4

Pressure at C is P0/4

Internal energies at A and B are the same

Temperature at C is T0/4

Solution:

Since the temperature is constant in process AB, it is isothermal process and hence no change in internal energy. ∴ΔUAB=0
Work done in process AB is WAB=nRT0 ln(V2/V1)=P0V0ln(4V0/V0)=P0V0ln(4)
Using VCTC=VBTB (since pressure is constant for process BC)
∴VoTC=4VoTo ⇒ TC=T0/4
Using VCPCTC=VAPATA where PA=P0
∴VoPCT0/4=VoP0To ⇒ PC=P0/4