A thermally insulated vessel

Question:

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 broght to rest. Assuming no heat is lost to the surroundings, its temperature increases by :-

  1. $\frac{\gamma \mathrm{Mv}^{2}}{2 \mathrm{R}}$

  2. $\frac{(\gamma-1)}{2 \mathrm{R}} \mathrm{Mv}^{2}$

  3. $\frac{(\gamma-1)}{2(\gamma+1) \mathrm{R}} \mathrm{Mv}^{2}$

  4. $\frac{(\gamma-1)}{2 \gamma \mathrm{R}} \mathrm{Mv}^{2}$

Correct Option: , 2

Solution:

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