Question

A one mole of an ideal gas expands adiabatically at constant pressure such that its temperature $ T \propto \frac{1}{\sqrt V} $ . The value of the adiabatic constant of gas is

• A. $ 1.3 $
• B. $ 1.5 $
• C. $ 1.67 $
• D. $ 2.0 $

Answer 1

Answer: (B)

In an adiabatic expansion,
$ PV^{\gamma} = $ constant
$ \because P = \frac{RT}{V} \quad $ (for $ 1 $ mole of gas )
$ \therefore (\frac{RT}{V})V^{\gamma} = $ constant
$ TV^{\gamma -1} = $ constant or $ T \propto V^{1-\gamma} $
As $ T \propto \frac{1}{\sqrt{V}} $
$ \therefore 1- \gamma = - \frac{1}{2} $
$ \gamma = 1 +\frac{1}{2} = \frac{3}{2} = 1.5 $