Physics - Heat & Thermo Question with Solution | TestHub

Let the insulated container has $n$ moles of the monoatomic gas. The loss of kinetic energy of the gas, $$\Delta E_K=\frac{1}{2}(mn)v^2$$ If the change in temperature of the gas is $\Delta T$, then heat gained by the gas is, $$\Delta Q=\frac{3}{2}nR\Delta T$$ Now, according to question, $$\begin{array}{rl}\Delta Q& =\Delta E_K\\ \frac{3}{2}nR\Delta T& =\frac{1}{2}mn{v}^2\\ \Rightarrow \Delta T& =\frac{m{v}^2}{3R}\end{array}$$