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Question

Certain amount of an ideal gas is contained in a closed vessel. The vessel is moving with a constant velcity 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

A
Mv2(γ1)/2R(γ+1)
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B
Mv2(γ1)/2R
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C
Mv2/2R(γ+1)
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D
Mv2/2R(γ1)
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Solution

The correct option is B Mv2(γ1)/2R
If m is the mass of the gas, then its kinetic energy
=12mv2

When the vessel is suddenly stopped, total kinetic energy will increase the temperature of the gas (because process will be adiabatic), i.e.,
=12mv2=nCvΔT
=mMCvΔT
mMR(γ1)ΔT=12mv2
(AsCv=R(γ1))

ΔT=Mv2(γ1)2R

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