• question_answer A gas expands adiabatically at constant pressure such that its temperature $T\,\propto \,a/\sqrt{V}.$ The value of $\gamma =({{C}_{p}}/{{C}_{V}})$ of the gas is A) 1.30      B) 1.50 C) 1.67 D) 2.00

 [b] In adiabatic expansion, $p{{V}^{\gamma }}=\,$constant put $p=\,\frac{RT}{V}$ $\left( \frac{RT}{V} \right)\,{{V}^{\gamma }}=\,\,\text{constant}\,\,$ $T{{V}^{\gamma -1}}=$constant or $T\propto \,{{V}^{1-\gamma }}$ $\because$     $T\propto \,\frac{1}{\sqrt{V}}$ $\therefore$    $1-\gamma =-\frac{1}{2}$ or         $\gamma =1+\frac{1}{2}\,=\frac{3}{2}\,=1.5$