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
Concept. When the vessel stops, the ordered KE of the gas becomes internal energy (insulated, no work). Per mole: $\tfrac12Mv^2=C_V\Delta T$ with $C_V=\dfrac{R}{\gamma-1}$.
Step 1. Solve. $\Delta T=\dfrac{Mv^2}{2C_V}=\dfrac{(\gamma-1)Mv^2}{2R}$.
Answer. Option C.
Solution by Sreeraj P, M.Sc Physics
