Q 11-11-016JEE MainAIEEE 2011Medium
A thermally insulated vessel contains an ideal gas of molecular mass $M$ and ratio of specific heats $\gamma$. It is moving with speed $v$ and is suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by
Answer: (C) $\dfrac{(\gamma - 1)}{2R}Mv^2$ K
The bulk kinetic energy of the gas becomes internal energy. For mass $m$ ($n = m/M$ moles):
$$\frac{1}{2}mv^2 = \frac{m}{M}\cdot\frac{R}{\gamma - 1}\Delta T \;\Rightarrow\; \Delta T = \frac{(\gamma - 1)Mv^2}{2R}$$
Solution by Sreeraj P, M.Sc Physics