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  4. A gas expands adiabatically at constant pressure such that its temperature T propto (1/√V) . The value of (Cp/Cv) of gas is

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Q. A gas expands adiabatically at constant pressure such that its temperature $T \propto \frac{1}{\sqrt{V}}$ . The value of $\frac{C_{p}}{C_{v}}$ of gas is

NTA AbhyasNTA Abhyas 2022

Solution:

$T \propto \frac{1}{\sqrt{V}}$
$TV^{\frac{1}{2}}=$ constant
For adiabatic process, $TV^{\gamma - 1}=$ const.
$\gamma -1=\frac{1}{2}$
$\therefore \, \gamma =\frac{3}{2}=1.50$