Question

In the reported figure, there is a cyclic process $ABCDA$ on a sample of $1\, mol$ of a diatomic gas. The temperature of the gas during the process $A \rightarrow B$ and $C \rightarrow D$ are $T_{1}$ and $T_{2}\left(T_{1} >T_{2}\right)$ respectively.

Choose the correct option out of the following for work done if processes $B C$ and $D A$ are adiabatic.

• A. $W_{A B}=W_{D C}$
• B. $W_{A D}=W_{B C}$
• C. $W_{B C}+W_{D A}>0$
• D. $W_{A B} < W_{C D}$

Answer 1

Answer: (B)

Work done in adiabatic process $=\frac{-n R}{\gamma-1}\left(T_{f}-T_{i}\right)$
$\therefore W_{A D}=\frac{-n R}{\gamma-1}\left(T_{2}-T_{1}\right)$
and $W_{B C}=\frac{-n R}{\gamma-1}\left(T_{2}-T_{1}\right)$
$\therefore W_{A D}=W_{B C}$