The P-V diagram of an ideal gas is as shown i | vedclass

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(C) The work done by the gas in a $P-V$ diagram is equal to the area under the curve.For process $AB$: The pressure is constant at $P_0$,and the volum

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$3P_0V_0$

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(C) The work done by the gas in a $P-V$ diagram is equal to the area under the curve.For process $AB$: The pressure is constant at $P_0$,and the volume changes from $2V_0$ to $V_0$. Work $W_{AB} = P_0(V_0 - 2V_0) = -P_0V_0$.For process $BC$: The volume is constant at $V_0$,and the pressure changes from $P_0$ to $2P_0$. Work $W_{BC} = 0$ (since $\Delta V = 0$).For process $CD$: The pressure is constant at $2P_0$,and the volume changes from $V_0$ to $3V_0$. Work $W_{CD} = 2P_0(3V_0 - V_0) = 2P_0(2V_0) = 4P_0V_0$.The total work done in the process $ABCD$ is $W_{ABCD} = W_{AB} + W_{BC} + W_{CD} = -P_0V_0 + 0 + 4P_0V_0 = 3P_0V_0$.

The $P-V$ diagram of an ideal gas is as shown in the figure. The work done by the gas in the process $ABCD$ is:

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