Thermodynamics

JEE Main level, single correct, medium

174 of 190

Question 174 of 190

A given ideal gas with γ=CpCv=1.5\gamma=\frac{C_p}{C_v}=1.5 at a temperature TT. If the gas is compressed adiabatically to one-fourth of its initial volume, the final temperature will be

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Answer: (C) 2T2 T

TVγ−1=T V^{\gamma-1}= constant
T1V1γ−1=T2V2γ−1⇒T(V)1/2=T2(V4)1/2[∵γ=1.5,T1=T,V1=V and V2=V4]∴T2=(4VV)1/2T=2T\begin{aligned} & T_1 V_1^{\gamma-1}=\mathrm{T}_2 V_2^{\gamma-1} \\ & \Rightarrow T(V)^{1 / 2}=\mathrm{T}_2\left(\frac{V}{4}\right)^{1 / 2} \\ & {\left[\because \gamma=1.5, T_1=T, V_1=V \text { and } V_2=\frac{V}{4}\right]} \\ & \therefore \quad T_2=\left(\frac{4 V}{V}\right)^{1 / 2} T=2 T \end{aligned}

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