Question

Work done in the cyclic process shown in the figure is -

• A. $4P_0{V}_0$
• B. $-4P_0{V}_0$
• C. $-\pi P_0{V}_0$
• D. $\pi P_0{V}_0$

Answer 1

The correct option is C $-\pi P_0{V}_0$

We know that,
Work done = Area under $P-V$ graph
Given, cyclic process is anticlockwise. So, area enclosed by it will be treated as negative.
$W=-\pi R_1{R}_2$
where $R_1$ and $R_2$ are the radii of the circle along Pressure and Volume axes (which will be equal in magnitude).
$\Rightarrow W=-\pi \left(\frac{3P_0-P_0}{2}\right)\times \left(\frac{3V_0-V_0}{2}\right)$
$\Rightarrow W=-\pi P_0{V}_0$
Thus, option (c) is the correct answer.