Question

The work done by gas in process ABCDEFGHA is

• A. $7P_o{V}_o$
• B. $-7P_o{V}_o$
• C. $9P_o{V}_o$
• D. $-9P_o{V}_o$

Answer 1

The correct option is C $9P_o{V}_o$

Work done : ${\int }_{v_1}^{v_2}Pdv$
We can decompose the path ABCDEFGHA into $AB-BC-CD-DE-EF-FG-GH-HA$
$W_{XY}=$ work done from X to Y
Since from A to B, pressure is $P_o$, $W_{AB}=P_o(V_o-3V_o)=-2P_o{V}_o$

Since there is no change in volume from B to C, $W_{BC}=0$
$W_{CD}=\left(4P_o\right)\left(3V_o\right)=12P_o{V}_o$
$W_{DE}=0$ in the same manner as $W_{BC}$
$W_{EF}=-4P_o{V}_o$
$W_{FG}=o$
$W_{GH}=3P_o{V}_o$
$W_{HA}=0$
Adding all, $W_{ABCDEFGHA}=9P_o{V}_0$