A thermally insulated vessel contains an ideal gas of molecular...

KE of the vessel $= \dfrac{1}{2}m{v}^{2}$

When the vessel is suddenly stopped, the ordered motion of the gas molecules is converted into disordered motion of the molecules increasing thereby the internal energy of the gas. Thus,

$∆ U = n{C}_{v} ∆ T = \dfrac{1}{2}m{v}^{2} = \dfrac{1}{2}\left(nM\right){v}^{2}$

Where $n$ is number of moles of the gas in the vessel and $M$ is molecular weight of the gas.

$∴ ∆ T = \dfrac{M{v}^{2}}{2{C}_{v}}$

As ${C}_{v} = \dfrac{R}{\gamma - 1}$

$∴ ∆ T = \dfrac{M{v}^{2} ( \gamma - 1 )}{2R} = \dfrac{M{v}^{2} ( 1 . 4 - 1 )}{2R} = \dfrac{M{v}^{2}}{5R}$