First slide

Law of equipartition of energy

Question

An insulated container containing monatomic gas of molar mass m is moving with a velocity v_o. If the container is suddenly stopped, find the change in temperature.

Moderate

A

$\frac{{mv}_{0}}{2 R}$
B

$\frac{{mv}_{0}^{2}}{3 R}$
C

$\frac{{mv}_{0}^{2}}{3 R^{2}}$
D

$\frac{{mv}_{0}^{2}}{4 R}$

Solution

If the container is stopped, then kinetic energy of atom in the container gets converted into heat.
$K . E . = \frac{1}{2} {μmv}_{0}$
Where v₀ is the velocity of the container and µ is the number of moles. It is converted into heat, then
$\frac{3}{2} μRΔT = \frac{1}{2} {μmv}_{0}^{2}$
or change in temperature $ΔT$ is given by $ΔT = \frac{{mv}_{0}^{2}}{3 R}$

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