A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats γ. It is moving with speed v and it suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by

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$\frac{(γ - 1)}{2 (γ + 1)} M ν^{2} K$

$\frac{(γ - 1)}{2 R} M ν^{2} K$

$\frac{(γ - 1)}{2 γ R} M ν^{2} K$

$\frac{γ M ν^{2}}{2 R} K$

answer is C.

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Detailed Solution

(3) As no heat is lost,

Loss of kinetic energy = gain of internal energy of gas

$\frac{1}{2} m v^{2} = n C_{v} ∆ T \Rightarrow \frac{1}{2} m v^{2} = \frac{m}{M} \cdot \frac{R}{γ - 1} ∆ T \Rightarrow ∆ T = \frac{M v^{2} (γ - 1)}{2 R} K$

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