Question

5.3)Theres a material.Initial state is(T_0,P_0).It is changed to (T,P) following solid-liquid coexistence line.Delta_V from melted solid is very small and L(latent heat) and delta_V are not related to Temperature.Find Solid-liquid coexistence equation on pressure-Temperature graph.

Answer 1

The Clausius-Clapeyron equation for the equilibrium between liquid and solid is given by:

dp/dT = L/(T(V_l-V_s))

where L is the latent heat of evaporation, and V_s and V_l are the specific volumes at temperature T of the solid and liquid phases, respectively.

Note that V_l is much greater than V_s so that

dp/dT = L/(TV_l)

Using perfect gas law,

dp/dT = L/(RT²/p)

(1/p)(dp/dT) = L/(RT²)

dp/p = (L/R)(dT/T²)

d(ln(p)) = (L/R)d(-1/T)

If L is independent of temperature then the solution to the differential equation is

ln(p/p₀) = c - (L/R)*[(1/T) - (1/T₀)]

Thsi is required equation.