CLAUSIUS-CLAPERYON тэгшитгэл

I. Review
The exact Clapeyron equation, dp/dT = DS/DV, was obtained for two-phase equilibrium in a one-component system.

II. Lecture topics
*A. Clapeyron Equation for solid-liquid and solid-solid equilibria
*B. Approximate Clausius-Clapeyron Equation for liquid-gas and solid-gas
–
d ln p/d (1/T) ~– –DH /R
C. Effect of hydrostatic pressureon vapor pressure
A. Clapeyron Equation for Condensed Phases
X(a) = X(b) in equilibrium at po, To; DG = 0
Ê dp ˆDS DH
Á˜ = = (1)
ËdT ¯coex DVTDV
DH=TDS=Hb – Ha, DV = Vb – Va
By choosing b to be the high-temperature phase, DH is always positive and the slope of the coexistence line depends on the sign of DV. For melting, most DV = Vliq –Vsol > 0 but in a few cases (H2O, Ga, Ge, Si, Bi) DV < 0. In many cases of solid-solid or solid-liquid, the coexistence line is approximately linear
Dp ~(DH /TDV)DT (2)

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