Latent Heat in Solid-->Liquid transitions (phase change)

[thonwer]

Homework Statement

Show that in Solid to Liquid transitions at [itex] T \ll {T}_{c} , L\simeq constant [/itex] where [itex] {T}_{c}, L [/itex] are the critic temperature and latent heat respectively.

Homework Equations

[itex] \left( \frac{d ( \frac {L} {T})} {dT} \right) = \frac {{c}_{p2}-{c}_{p1}} {T}+ \frac {\alpha_1v_1-\alpha_2v_2} {v_2-v_1} \frac {L} {T} [/itex]

2 is for liquid and 1 is for solid
cp,α are the calorific coefficient at constant pressure and the cubic expansion coefficient.

The Attempt at a Solution

For example with ice and water, I assume [itex] v_2 \simeq v_1 [/itex] and then I try to solve the differential equation but I don't get to [itex] L\simeq constant [/itex].

Can anybody help me please?

 

[Chestermiller]

Consider using the Clapyron equation which relates the changes in pressure and temperature along the equilibrium line between solid and liquid.

Chet