Question

In the cyclic process shown in P-V diagram, the magnitude of the work done is

• A. $\pi \left(\frac{P_{2} - P_{1}}{2}\right)^{2}$
• B. $\pi \left(\frac{V_{2} - V_{1}}{2}\right)^{2}$
• C. $\frac{\pi }{4}\left(\right.P_{2}-P_{1}\left.\right)\left(\right.V_{2}-V_{1}\left.\right)$
• D. $\pi\left( V _{2}- V _{1}\right)^{2}$

Answer 1

Answer: (C)

Work done = Area bounded by the circle

$=\pi \frac{\left(\right. P_{2} - P_{1} \left.\right)}{2}\frac{\left(\right. V_{2} - V_{1} \left.\right)}{2}$

$=\frac{\pi }{4}\left(\right.P_{2}-P_{1}\left.\right)\left(\right.V_{2}-V_{1}\left.\right)$