Question

In the cyclic process shown in the $ P $ - $ V $ diagram calculate the work done.

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

Answer 1

Answer: (C)

Work done = area enclosed by the cycle consider cycle to be an ellipise
$\therefore $ Area $=x\left[\frac{P_{2}-P_{1}}{2}\right] \left[\frac{V_{2}-V_{1}}{2}\right]$
$=\frac{\pi}{4}\left(p_{2}-P_{1}\right)\left(V_{2}-V_{1}\right)$