Question

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

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

Answer 1

Answer: (B), (C)

Work done by the gas in process AB is $P_0{V}_0$ ln 4

AB is an isothermal process.
$\Rightarrow \text{Internal energy at A = Internal energy at B.}$

Applying
$\frac{PV}{T}$
= constant between A and B
$\frac{P_0{V}_0}{T_0}=\frac{P_{B}4V_0}{T_0}\Rightarrow P_B=\frac{P_0}{4}$

As it is not clearly indicated that BC is passing through origin, prediction about point C is not possible.