Question

An ideal gas is taken around the cycle ABCA as shown in P-V diagram.

The net work done by the gas during the cycle is equal to:

• A. $12P_1{V}_1$
• B. $6P_1{V}_1$
• C. $3P_1{V}_1$
• D. $P_1{V}_1$

Answer 1

Answer: (C)

Step 1:

For a P-V diagram,

work done = area enclosed by the figure

$\therefore W_{ABCA}=\text{area enclosed by the fig.}ABCA$

$\because$ ABC is a $△$.

Step 2:

$\therefore W_{ABCA}=\frac{1}{2}\times (3V_1-V_1)(6P_1-P_1)$

$\Rightarrow W_{ABCA}=\frac{1}{2}\times 2V_1\times 5P_1=5P_1{V}_1$

Hence, the net work done by the gas during the cycle is equal to $5P_1{V}_1$.

Therefore, option (C) is correct.