The molar specific heat at constant pressure of an ideal gas is ($\frac{7}{2}$) R. The ratio of specific heat at constant pressure to that at constant volume is:

We have given molar specific heat at constant pressure

         ${\mathrm{C}}_{\mathrm{p}}= \frac{7}{2}\mathrm{R}$

We know ${\mathrm{C}}_{\mathrm{p}}-{\mathrm{C}}_{\mathrm{v}} = \mathrm{R}$

$\Rightarrow {\mathrm{C}}_{\mathrm{V}} = {\mathrm{C}}_{\mathrm{p}}-\mathrm{R} = \frac{7}{2}\mathrm{R}-\mathrm{R} = \frac{5}{2}\mathrm{R}$

Hence, required ratio is

$\mathrm{\gamma } = \frac{{\mathrm{C}}_{\mathrm{p}}}{{\mathrm{C}}_{\mathrm{v}} } = \frac{\left({\displaystyle \frac{7}{2}}\right)\mathrm{R}}{\left({\displaystyle \frac{5}{2}}\right)\mathrm{R}} = \frac{7}{5}$