Question

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

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

Answer 1

The correct option is B $\frac{3P_o{V}_o}{4}$

For one mole of gas $KE=\frac{3}{2}RT$

Given $P=\frac{P_o}{1+(\frac{V}{V_o}{)}^3}$
when $V=V_o$
$P=\frac{P_o}{2}$

Using Ideal gas equation,
$PV=nRT$ where $n=1$
$\Rightarrow T=\frac{P_o{V}_o}{2R}$

Substituting $T$ in $KE$ expression we get,
$KE=\frac{3P_o{V}_o}{4}$