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

In isothermal process dPdVIsotherm=-PV---(1)In adiabatic processdPdVAdiabatic=-γPV---(2)From equation (2) divided by equation(1 )⇒Ratio=slope of adiabatic processslope of isothermal process ⇒Ratio=-γPV-PV ⇒Ratio=γ