An ideal gas expands isothermally from a volume $V_1$ to $V_2$ and then compressed to original volume $V_1$ adiabatically. The initial pressure is $P_1$ and final pressure is $P_3$. The total work done is $W$. Then:

• A

  $P_3>P_1, W>0$
• B

  $P_3<P_1, W<0$
• Correct answer
  C

  $P_3>P_1, W<0$
• D

  $P_3=P_1, W=0$

Solution

From the graph it is clear that $P_3>P_1$ .
Since the area under adiabatic process $\left(\mathrm{B}\mathrm{C}\mathrm{E}\mathrm{D}\right)$ is greater than that of the isothermal process $\left(\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}\right)$ . Therefore net word done
$W=W_{\mathrm{i}}+\left(-W_A\right)$
$\because W_{\mathrm{A}}>W_{\mathrm{i}}\Rightarrow W<0$

Hence, the correct answer is option: 'C'.