Question

$P-V$ diagram of an ideal gas is shown in the figure. Work done by the gas in process $ABCD$ is

• A. $4P_0{V}_0$
• B. $2P_0{V}_0$
• C. $3P_0{V}_0$
• D. $P_0{V}_0$

Answer 1

The correct option is C $3P_0{V}_0$

From the given $P-V$ diagram, it can be observed that,
$A\to B$ is an Isobaric process; $B\to C$ is an Isochoric process; $C\to D$ is an Isobaric process.
Work done during process $AB$, $\left(W_{AB}\right)=P\times \Delta V=-P_0{V}_0$
Similarly,
Work done during process $BC$, $\left(W_{BC}\right)=0$
Work done during process $CD$, $\left(W_{CD}\right)=4P_0{V}_0$
$\Rightarrow$ Total work done in process $ABCD$ is
$W_{ABCD}=W_{AB}+W_{BC}+W_{CD}=-P_0{V}_0+0+4P_0{V}_0=3P_0{V}_0$
Hence, option (c) is the correct answer.