MHTCET 16 Apr 2026 Shift 2 Paper

Concept:When the moving insulated container stops, its bulk kinetic energy is converted into internal energy of the gas, raising its temperature.Explanation:A rigid diatomic gas has 5 degrees of freedom: 3 translational and 2 rotational.Therefore, the molar heat capacity at constant volume is:$$C_V = \frac{5R}{2}$$Let the number of moles of gas be $n$.Total mass of the gas is:$$M = nm$$The bulk kinetic energy of the moving container and gas is:$$\frac{1}{2}MV^2 = \frac{1}{2}nmV^2$$Since the container is insulated, no heat is lost to the surroundings.When stopped suddenly, this kinetic energy heats the gas:$$nC_V \Delta T = \frac{1}{2}nmV^2$$Substitute $C_V = \frac{5R}{2}$:$$n\left(\frac{5R}{2}\right)\Delta T = \frac{1}{2}nmV^2$$Cancelling $n$ and $\frac{1}{2}$ from both sides:$$5R\Delta T = mV^2$$Therefore:$$\Delta T = \frac{mV^2}{5R}$$Answer:$$\Delta T = \frac{mV^2}{5R}$$Hence, the correct option is C.