TABLE OF CONTENTS 14.1. (a) Show that in a first order phase transition
where L is the latent heat and C 1 and C 2 are the heat capacities of the higher and lower temperature phases respectively, measured along the coex istence curve. One way to prove this is to consider 1 kmole of the substance going round the following closed cycle. The substance starts in phase 1 on the coexistence curve at temperature T. It is transformed to phase 2, and is then heated from T to T+ dT, the pressure changing to remain on the coexistence curve. At this temperature, it is transformed back to phase 2, and cooled along the coexistence curve to its starting point. Since the cycle is reversible, the overall change of entropy round the cycle must be zero.
(b) Show that if phase 1 is an ideal gas, while phase 2 is a liquid or solid of negligible volume, Equation (14.43) becomes
where C p 1 and C p 2 are the respective heat capacities at constant pressure. (c) Under the same assumptions as (b), show that C 1<0 if L ? R 0 T (as is usually the case for a gas-liquid transition except very close to the critical point). Explain why this is the case, and show that it does not contradict the second law of thermodynamics, which requires that C V and C p be positive for...
