Kinetic Theory

JEE Main level, single correct, medium

73 of 168

Question 73 of 168

During an adiabatic process, if the pressure of a gas is found to be proportional to the cube of its absolute temperature, then the ratio of CPCV\frac{C_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}} for the gas is :

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Answer: (C) 32\frac{3}{2}

$\begin{aligned}
& \mathrm{P} \propto \mathrm{T}^3 \\
& \mathrm{PT}^{-3}=\text { constant } \\
& \because \frac{\mathrm{PV}}{\mathrm{T}}=\mathrm{nR}=\text { constant from ideal gas equation } \\
& (\mathrm{P})(\mathrm{PV})^{-3}=\text { constant } \\
& \mathrm{P}^{-2} \mathrm{~V}^{-3}=\text { cosntant }...(i)
\end{aligned}$
∵\because Process equation for adiabatic process is
PVy= constant ...(ii)\mathrm{PV}^{\mathrm{y}}=\text { constant }...(ii)
Comparing equation (1) and (2)
CPCV=y=32\frac{C_P}{C_V}=y=\frac{3}{2}

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