Kinetic Theory

JEE Main level, single correct, medium

163 of 168

Question 163 of 168

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

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Answer: (C) (γ−1)2RMv2 K\frac{(\gamma-1)}{2 \mathrm{R}} \mathrm{Mv}^2 \mathrm{~K}

W=ΔU\mathrm{W}=\Delta \mathrm{U}
12mv2=nCvdT\frac{1}{2} \mathrm{mv}^2=\mathrm{nC}_{\mathrm{v}} \mathrm{dT}
=mMRγ−1dT=\frac{\mathrm{m}}{\mathrm{M}} \frac{\mathrm{R}}{\gamma-1} \mathrm{dT}
dT=M(γ−1)v22RK\mathrm{dT}=\frac{\mathrm{M}(\gamma-1) \mathrm{v}^2}{2 \mathrm{R}} \mathrm{K}

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