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

Solution :
We have given molar specific heat at instant pressure $${C_p} = \frac{7}{2}R$$
Mayer's relation can be written as :
Molar specific heat at constant pressure - Molar specific heat at constant volume = Gas constant,
$$\eqalign{ & {\text{i}}{\text{.e}}{\text{.}}\,{C_p} - {C_V} = R \Rightarrow {C_V} = {C_p} - R \cr & = \frac{7}{2}R - R = \frac{5}{2}R\left[ {\because {C_p} = \frac{7}{2}R} \right] \cr} $$
Hence, required ratio is $$\gamma = \frac{{{C_p}}}{{{C_V}}} = \frac{{\left( {\frac{7}{2}} \right)R}}{{\left( {\frac{5}{2}} \right)R}} = \frac{7}{5}$$