1. The problem statement, all variables and given/known data a) Starting from the statement that total entropy (Ssystem+Ssurr) can only increase, show that G = U - TS +pV will attain its minimum value for a system in equilibrium with a fixed pressure and temperature reservoir. b)At atmospheric pressure, a particular substance is found to undergo a discontinuous change between two states at temperature TC when heated. Its volume increases by ΔV and it absorbs latent heat L as its temperature is changed from just below TC to just above TC. Explain why at TC, the value of G is the same for the two states with different volumes. c)Explain why L must be positive and comment on whether TC is expected to increase or decrease with pressure. 2. Relevant equations Clausius-Clapyeron Equation 3. The attempt at a solution a)Taking the differential of the given equation, I get dG = dU - TdS -SdT +pdV + Vdp. Eliminate two terms because the system is in thermal equilibrium at constant pressure/temperature. This gives dG = dU - TdS + pdV = 0 using the first law. Hence G is mimimum when the boundary conditions of the system permit a constant pressure/temperature environment. I did not really use the fact that the total S ≥ 0 though, so is there another derivation? b)So is this process occurring at constant pressure and is TC the value of T on the boundary line between the two phases at that particular pressure? If the case, then at TC the two phases instantaneously have the same pressure/temperature. dG = Vdp - SdT = 0, so G is constant over the boundary line. c) V increases upon heating at constant pressure. So I would imagine this would correspond to an increase in entropy of the system. So l = T(S2-S1) > 0. dP/dT is usually +ve for most substances. So dT/dP is decreasing, so in most cases expect TC to decrease with pressure. Did I do this right? Many thanks.