Question

In the cyclic process shown 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. $\frac{\pi }{4}(P_2-P_1)(V_2-V_1)$
• D. $\pi (P_2{P}_1-V_2{V}_1)$

Answer 1

Answer: (C)

$\frac{\pi }{4}(P_2-P_1)(V_2-V_1)$

Work done(W)=Area under the P-V curve=$\frac{\pi }{4}(P_2-P_1{)}^2(V_2-V_1)=\pi \times {\left(\frac{P_2-P_1}{2}\right)}^2=\frac{\pi }{4}(V_2-V_1{)}^2=\pi \times {\left(\frac{V_2-V_1}{2}\right)}^2=\frac{\pi }{4}(P_2-P_1)(V_2-V_1)$