Question

One mole of a diatomic gas undergoes a process $P=\frac{P_0}{1+{\left(\frac{V}{V_0}\right)}^3}$, where $P_0,V_0$ are constants. The translational kinetic energy of the gas when $V=V_0$ is given by

• A. $\frac{5P_0{V}_0}{4}$
• B. $\frac{3P_0{V}_0}{4}$
• C. $\frac{3P_0{V}_0}{2}$
• D. $\frac{5P_0{V}_0}{2}$

Answer 1

The correct option is B $\frac{3P_0{V}_0}{4}$

$P=\frac{P_0}{1+{\left(\frac{V}{V_0}\right)}^3}=\frac{P_0}{2}\Rightarrow T=\frac{P_0{V}_0}{2R}$

$\therefore$ Translational kinetic energy is equal to $\frac{3}{2}RT=\frac{3R}{2}\frac{P_0{V}_0}{2R}=\frac{3P_0{V}_0}{4}$