The ratio of the slopes of P-V graphs of adiabatic and isothermal process is(in terms of specific heat ratio $\gamma$)

In isothermal process ${\left(\frac{\text{dP}}{\text{dV}}\right)}_{\text{Isotherm}}\text{=}\frac{\text{-P}}{\text{V}}\text{---(1)}$

In adiabatic process${\left(\frac{\text{dP}}{\text{dV}}\right)}_{\text{Adiabatic}}\text{=}\frac{\text{-γP}}{\text{V}}\text{---(2)}$

From equation (2) divided by equation(1 )

$$\begin{gathered} \Rightarrow Ratio=\frac{slope of adiabatic process}{slope of isothermal process} \\ \Rightarrow Ratio=\frac{{\displaystyle \frac{-\gamma P}{V}}}{\frac{-P}{V}} \\ \Rightarrow Ratio=\gamma \end{gathered}$$