First slide

Internal 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 and temperature is T. Find kinetic energy of the gas with respect to centre of mass and with respect to ground.

Moderate

Solution

By law of equipartition of energy,
Energy of gas at temperature T is = $\frac{f n R T}{2}$
Here, f = 5.
So, $E = \frac{5 n R T}{2}$ .
This energy is with respect to centre of mass.
For finding energy with respect to ground, an extra factor of $\frac{1}{2} M v^{2}$ need to be added.

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