Question

One mole of an ideal monoatomic gas is taken through a semi-circular thermodynamic process ACB shown in the P – V diagram. The heat supplied to the system is

• A. $P_0^2\left(\frac{5+\pi }{2}\right)$
• B. $P_0{V}_0\left(\frac{2\pi -1}{2}\right)$
• C. $P_0{V}_0(1+\pi )$
• D. $P_0{V}_0\left(\frac{5+\pi }{2}\right)$

Answer 1

The correct option is D

$P_0{V}_0\left(\frac{5+\pi }{2}\right)$

$\Delta W=P_0{V}_0+\frac{1}{2}\pi 2P_0{V}_0\times \frac{1}{2}=P_0{V}_0(1+\frac{\pi }{2})$

$\Delta U=\frac{3}{2}(P_{0}2V_0-P_0{V}_0)=\frac{3}{2}{P}_0{V}_0$

$\Delta Q=P_0{V}_0(1+\frac{\pi }{2}+\frac{3}{2})=P_0{V}_0\left(\frac{5+\pi }{2}\right)$