During an adiabatic process of an ideal gas, if $$P$$ is proportional to $$\frac{1}{{\;{V^{1.5}}}},$$  then the ratio of specific heat capacities at constant pressure to that at constant volume for the gas is

Solution :
$$\eqalign{ & {\text{As}}\,\,P \propto \frac{1}{{\;{V^{1.5}}}},\,{\text{So}}\,\,P{V^{1.5}} = {\text{constant}} \cr & \therefore \gamma = 1.5\,\,\left( {\because {\text{Process}}\,{\text{is}}\,{\text{adiabatic}}} \right) \cr & {\text{As}}\,{\text{we}}\,{\text{know,}}\,\,\frac{{{C_p}}}{{{C_v}}} = \gamma \cr & \therefore \frac{{{C_p}}}{{{C_v}}} = 1.5 \cr} $$