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Formula and Calculation

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State all of the assumptions (e.g. ideal gas etc).
(a) Starting with dGm = VmdP-SmdT, derive the relationship (Clayperon Equation) that expresses the slopes between the solid/liquid/gas phase boundaries in a Pressure versus Temperature plot.

(b) Using the Clayperon equation from part a, justify the difference in the solid-liquid phase boundary for water versus most other material.

(c) From the equation derived in part a, show how the Clausius-Clayperon equation is derived for the liquid-gas or solid-gas phase boundary where ideal gas conditions are assumed

(d) Given the change in Hboiling for water at 1 atm of pressure is 44Kj/mole, calculate the boiling point temperature for water in a pressure cooker at 1.5 atm. (R=8.314 J/Kmole).

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The solution examines formula and calculations for the given problems.

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a. dGm = VmdP-SmdT
dGm(1) = dGm(2)
Vm(1)dp - Sm(1)dT = Vm(2)dp - Sm(2)dT
{Vm(2) - Vm(1)}dp = {Sm(2) - Sm(1)}dT
ΔtrsVdp = ΔtrsSdT
For a closed system undergoing an internally reversible process, the first law is: du = ɗq + ɗw = Tds - Pdv
Using the definition of specific enthalpy, h, and the fact that the temperature and pressure are constant, we have: du + Pdv = dh = Tds → ds = dh/T → ΔtrsS = Δh/T
We thus substitute for ΔtrsS as follows:
T Δ trsVdp = ...

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