An insulated box containing a diatomic gas of molar mass $M$ is moving with a velocity $v$. If the box is suddenly stopped, the resulting change in temperature is ($R$ is the gas constant)

The correct option is C.

Let $n$ be the number of moles of the gas in the box.

The kinetic energy of the gas = $n\left(\frac{1}{2}M{v}^2\right)$.............(i)

When the box is suddenly stopped, this energy is used up in changing the internal energy, as a result of which the temperature of the gas rises.

The change in internal energy is given by$\Delta U=n{C}_v\Delta T$..........(ii)

For a diatomic gas $C_v=\frac{5}{2}R$

Hence from equation (i) and (ii) we get,

$n\times \frac{5R}{2}\times \Delta T=n\times \frac{1}{2}M{v}^2$

Or $\Delta T=\frac{M{v}^2}{5R}$, which is choice (c).