PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
For an ideal gas, consider a reversible adiabatic curve and an isothermal curve that pass through the same point (P,V) in the P–V plane.
(i) Starting from the appropriate thermodynamic relations, obtain the slope dP/dV of the adiabatic curve at that point and show that, on a log P versus log V plot, the slope of the adiabatic curve is −γ.
(ii) Find the corresponding slope for the isothermal curve on the same log–log plot and hence prove that the adiabatic curve is steeper than the isothermal curve.
(iii) Explain physically why the difference in slopes arises for an ideal gas.