Question

Two moles of an ideal gas have undergone a cyclic process $1 \, - \, 2 \, - \, 3 \, - \, 1$ . If net heat exchange in the process is $-300 \, J$ , then work done by the gas in the process $2-3$ is $\left(R = 8.3 \, J m o l^{- 1} K^{- 1}\right)$

• A. $-5000 \, J$
• B. $5000 \, J$
• C. $-3000 \, J$
• D. none of these

Answer 1

Answer: (D)

The process 1-2 is isobaric therefore work done by the gas is
$W_{1 \rightarrow 2}=nR\Delta T=2\times R\times 300$
$W_{1 \rightarrow 2}=600R=4980 \, J$
The process 3-1 is isochoric therefore work done by the gas is zero.
Therefore,
$W_{1 \rightarrow 2 \rightarrow 3 \rightarrow 1}=W_{1 \rightarrow 2}+W_{2 \rightarrow 3}$
Also for cyclic process,
$\Delta W=\Delta Q$
$W_{1 \rightarrow 2}+W_{2 \rightarrow 3}+0=\Delta Q$
$4980J +W_{2 \rightarrow 3}=-300J$
$W_{2 \rightarrow 3}=-5280J$