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

Certain amount of an ideal gas is contained in a closed vessel. The vessel is moving with a constant velocity v. The rise in temperature of the gas when the vessel is suddenly stopped is (M is molecular mass, g = Cp/Cn)

A

Mv2(γ1)2R\frac{Mv^{2}(\gamma - 1)}{2R}

B

Mv2(γ+1)2R\frac{Mv^{2}(\gamma + 1)}{2R}

C

Mv22Rγ\frac{Mv^{2}}{2R\gamma}

D

Mv22R(γ+1)\frac{Mv^{2}}{2R(\gamma + 1)}

Answer

Mv2(γ1)2R\frac{Mv^{2}(\gamma - 1)}{2R}

Explanation

Solution

12\frac{1}{2}MV2 = msDQ &

(s)gm = CmolarM\frac{C_{molar}}{M} & [Cv=Rγ1]\left\lbrack C_{v} = \frac{R}{\gamma - 1} \right\rbrack