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JEE Main 2011 (AIEEE) · Degrees of Freedom & Internal Energy

Degrees of Freedom & Internal Energy question from JEE Main 2011 (AIEEE)

Q39JEE Main 2011 · AIEEEMedium

Degrees of Freedom & Internal Energy

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 it's suddenly brought to rest. Assuming no heat is lost to the surroundings, Its temperature increases by:

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Answer: (c)

Per mole: $\frac{1}{2}Mv^2 = C_v\Delta T$ with $C_v = \frac{R}{\gamma-1}$ .
$\Delta T = \frac{Mv^2(\gamma-1)}{2R}$
So the answer is (c) $\frac{(\gamma-1)}{2R}Mv^2$ K.

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