A gas expands adiabatically at constant pressure such that $\mathrm{T} \propto \mathrm{V}^{-1 / 2}$. The…

A gas expands adiabatically at constant pressure such that $\mathrm{T} \propto \mathrm{V}^{-1 / 2}$. The value of $\gamma\left(\mathrm{C}_{\mathrm{p}, \mathrm{m}} / \mathrm{C}_{\mathrm{vm}}ight)$
of the gas will be :
  1. $1.30$
  2. $1.50$
  3. $1.70$
  4. 2

Solution

$\mathrm{T} \propto \frac{1}{\sqrt{\mathrm{V}}} ; \mathrm{TV}^{1 / 2}=\mathrm{constant}$
For adiabatic process, $\mathrm{TV}^{\gamma-1}=$ constant
$\therefore \gamma-1=\frac{1}{2}, \gamma=\frac{3}{2}$

Asked in: JEE-TOPICTESTS-CHEMISTRY

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