An insulated container containing monoatomic gas of molar mass m is moving with a velocity ${\mathrm{v}}_{\mathrm{o}}$. If the container is suddenly stopped, find the change in temperature.

detailed solution

Correct option is B

When, the container stops, its total kinetic energy is transferred to gas molecules in the form of translational kinetic energy, thereby increasing theabsolute temperature.Assuming n = number of molesGiven, m = molar mass of the gas.If ∆T = change in absolute temperatureThen, kinetic energy of molecules due to velocity vo,∆Kmotion = 12(mn)v02-----------------(i)Increase in translational kinetic energy∆Ktranslation = n32R(∆T)------------(ii)According to kinetic theory Eqs. (i) and (ii) are equal⇒ 12(mn)v02 = n32R(∆T)(mn)v02 = n3R(∆T)⇒∆T = (mn)v023nR = mv023R