MHTCET 11 May 2024 Shift 1 Paper

Concept:When the moving insulated container is stopped suddenly, its macroscopic kinetic energy is converted into the internal energy of the gas, which raises the temperature.Explanation:Let $n$ be the number of moles of the diatomic gas and $m$ be its molar mass.Total mass of the gas is $M = n m$.Initial kinetic energy of the container is:$$KE = \frac{1}{2}M V^2 = \frac{1}{2}n m V^2$$Since the container is insulated, no heat is lost, so this kinetic energy equals the change in internal energy of the gas:$$\Delta U = n C_v \Delta T$$For a diatomic gas, the molar specific heat at constant volume is:$$C_v = \frac{5}{2}R$$Using energy conservation:$$n \cdot \frac{5}{2}R \cdot \Delta T = \frac{1}{2}n m V^2$$Cancelling $n$ from both sides and solving for $\Delta T$:$$\frac{5}{2}R \Delta T = \frac{1}{2}m V^2$$$$\Delta T = \frac{m V^2}{5R}$$Answer:$$\Delta T = \frac{mV^2}{5R}$$Hence, the correct option is B.