Q. 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
A) $\frac{(\gamma - 1)}{2(\gamma + 1)R}Mv^{2}$
B) $\frac{(\gamma - 1)}{2\gamma R}Mv^{2}$
C) $\frac{\gamma Mv^{2}}{2R}$
D) $\frac{(\gamma - 1)}{2R}Mv^{2}$
Explanation
(d) $\frac{1}{2}Mv^{2} = C_{V}.\mathrm{\Delta}T$
$\frac{1}{2}Mv^{2} = \frac{R}{\gamma - 1}.\mathrm{\Delta}T \Rightarrow \mathrm{\Delta}T = \frac{M.v^{2}(\gamma - 1)}{2R} = \frac{(\gamma - 1)Mv^{2}}{2R}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.