Question

One mole of an ideal gas in initial state A undergoes a cyclic process ABCA as shown in the figure if pressure at A is $P_0$. Choose the correct option(s) from the following:

• A. Internal energies at A and B are the same
• B. Work done by the gas in process AB is $P_0{V}_0$ log 4
• C. Pressure at C is $\frac{P_0}{4}$
• D. Temperature at C is $\frac{T_0}{4}$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A Internal energies at A and B are the same
B Work done by the gas in process AB is $P_0{V}_0$ log 4
C Pressure at C is $\frac{P_0}{4}$
D Temperature at C is $\frac{T_0}{4}$

Process A $\to$ B is isothermal, So $U_A=U_B$

$W_{AB}=nRTin\frac{V_2}{V_1}=R{T}_{0}In\frac{4V_0}{V_0}$

$=P_0{V}_{0}log4[P_0{V}_0=R{T}_{0}forn=1]$

$\frac{P_0{V}_0}{T_0}\left(atA\right)=\frac{P_{c}4V_0}{T_0}\left(atC\right)$

$\Rightarrow P_c=\frac{P_0}{4}$