Methane has a triple point at T₃ = 90.67 K and P₃ = 0.117 bar. The atmospheric pressure at the surface of Saturns moon Titan is P 1.5 bar, at an average surface temperature of T 94 K.

(a)

i. Determine the boiling point of methane on Titans surface, given its latent heat of vapourization is 8190 J mol¹ K¹ .

ii. With the aid of a phase diagram, explain that methane lakes are expected on Titan.

(b) Show that the decrease in Helmholtz free energy during the evaporation of a methane lake is nRT.

(c) Explain what happens to the entropy of a cloud of methane vapour as it starts to rain, and why this is not in contradiction with the Second Law of Thermodynamics.