A liquid is at equilibrium with its vapour. The vapour is assumed to be an ideal gas. The liquid has a molar latent heat of vaporisation ℓ_ℓg that depends on temperature, with ℓ_ℓg = A − BT, where A and B are constants. Apply the Clausius–Clapeyron relation (6.50) and consider that the molar volume of the liquid phase is negligible compared to the vapour phase, i.e. v_ℓ ≪ v_g. Use the ideal gas law (5.47) for the vapour phase. Show that at equilibrium at a temperature T, the vapour pressure p depends on temperature according to Dupré’s law,

where p₀ is the vapour pressure at T₀.

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P A 1 B T In - ( ² ) = ² ( 71 - 7) - ² + ¹ ( 7 ) In Po R To T R To