Question

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

Answer 1

As container is insulated there is no heat loss to ambient.

Loss in kinetic energy due to sudden stop,

$\Delta KE=(\frac{1}{2}M{v}_o^2=\frac{1}{2}(mn\left)v_o^2\right))$

This loss in kinetic energy will increase the internal energy of the gas (the internal energy $E$ of an ideal gas is purely kinetic i.e., translational kinetic energy)

$\Delta E=\Delta U=\frac{3}{2}nR\Delta T$

Loss in kinetic energy = increase in translational kinetic energy

$\frac{1}{2}\left(mn\right)v_o^2=\frac{3}{2}nR\Delta T$

$\Delta T=\frac{m{v}_o^2}{3R}$

$\text{Final Answer}:\Delta T=\frac{m{v}_o^2}{3R}$.