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Q.

Certain amount of an ideal gas is contained in a closed vessel. The vessel is moving with a constant velocity v. The molecular mass of gas is M. The rise in temperature of the gas when the vessel is suddenly stopped is γ=CP/CV

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a

Mv2(γ−1)2R(γ+1)

b

Mv2(γ−1)2R

c

Mv22R(γ+1)

d

Mv22R(γ−1)

answer is B.

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Detailed Solution

If m is the total mass of the gas, then its kinetic energy =1/2mv2 When the vessel is suddenly stopped, total kinetic energy will increase the temperature of the gas (because process will be adiabatic), i.e.,    12mv2=μCvΔT=mMCvΔT⇒mMRγ−1ΔT=12mv2      As Cv=Rγ−1⇒ΔT=Mv2(γ−1)2R
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