Certain amount of an ideal gas are 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
Mv22R(γ+1)
b
Mv2(γ−1)2R
c
Mv22R(γ+1)
d
Mv2R(γ+1)
answer is B.
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Detailed Solution
If m is the total mass of the gas then its kinetic energy =12mv2When the vessel is suddenly stopped then total kinetic energy will increase the temperature of the gas. Hence 12mv2=μCvΔT=mMCvΔT [As Cv=Rγ−1⇒mMRγ−1ΔT=12mv2⇒ΔT=Mv2(γ−1)2R
Certain amount of an ideal gas are 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)