First slide

Law of equipartition of energy

Question

A light container having a diatomic gas enclosed within is moving with velocity V. mass of the gas is M and number of moles is n. the kinetic energy of gas with respect to ground is

Moderate

A

$\frac{1}{2} M V^{2} + \frac{3}{2} n R T$
B

$\frac{1}{2} M V^{2}$
C

$\frac{1}{2} M V^{2} + \frac{5}{2} n R T$
D

$\frac{5}{2} n R T$

Solution

The kinetic energy of gas with respect to COM of the system is $\frac{5}{2} n R T$
Kinetic energy of gas w.r.t ground = kinetic energy of COM w.r.t ground + kinetic energy of gas w.r.t COM
$K . E . = \frac{1}{2} M V^{2} + \frac{5}{2} n R T$

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