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JEE Main 2011
Exam
JEE Main
Year
2011
Subject
Physics
Chapter
Kinetic Theory of Gases

JEE Main 2011 · Physics · Kinetic Theory of Gases

A thermally insulated vessel contains an ideal gas of molecular...

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 :

Options

  1. A(γ−1)2γRMv2 K\frac{(\gamma-1)}{2 \gamma \mathrm{R}} \mathrm{Mv}^2 \mathrm{~K}
  2. BγMv22RK\frac{\gamma M v^2}{2 \mathrm{R}} \mathrm{K}
  3. C(γ−1)2RMv2 K\frac{(\gamma-1)}{2 \mathrm{R}} \mathrm{Mv}^2 \mathrm{~K}
  4. D(γ−1)2(γ+1)RMv2 K\frac{(\gamma-1)}{2(\gamma+1) R} \mathrm{Mv}^2 \mathrm{~K}

Correct answer

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

Step-by-step solution

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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