Question

Energy of all molecules of a monatomic gas having a volume $V$ and pressure $P$ is $\frac{3}{2}PV$. The total translational kinetic energy of all molecules of a diatomic gas at the same volume and pressure is

• A. $\frac{1}{2}PV$
• B. $\frac{3}{2}PV$
• C. $\frac{5}{2}PV$
• D. $3PV$

Answer 1

Answer: (B)

$\frac{3}{2}PV$

total kinetic energy
$E_t=\frac{f}{2}PV$
where
$f=\text{degree of freedom}$
$P=Pressure$
$V=volume$
for momatomic gas f = 3
so $E_t=\frac{3}{2}PV$
for diatomic gas f=5, out of which 3 are translatory degree of freedom and 2 are rotational
degree of freedom.
by Maxwell's Law Of Equipartition of Energy , total energy is shared equally among all degree of freedom
so translation kinetic energy = $\frac{3}{5}{E}_t$

= $\frac{3}{5}\times \frac{5}{2}PV$

= $\frac{3}{2}PV$
answer is B.