For an ideal gas, reversible isothermal and reversible adiabatic processes are described by the relations PV=constant and PVγ=constant respectively, where γ>1.
(i) Starting from the respective relations, obtain an expression for the slope (dVdP) of each curve on a P–V diagram in terms of P and V at an arbitrary point on the curve.
(ii) Show that, for the same values of P and V, the magnitude of the slope for the adiabatic curve exceeds that for the isothermal curve by a factor of γ.
(iii) Hence explain, with physical reasoning based on the First Law of Thermodynamics, why the adiabatic curve is qualitatively steeper than the isothermal curve throughout the diagram.