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

1. Jan 7, 2015

thonwer

1. The problem statement, all variables and given/known data
Show that in Solid to Liquid transitions at $T \ll {T}_{c} , L\simeq constant$ where ${T}_{c}, L$ are the critic temperature and latent heat respectively.
2. Relevant equations
$\left( \frac{d ( \frac {L} {T})} {dT} \right) = \frac {{c}_{p2}-{c}_{p1}} {T}+ \frac {\alpha_1v_1-\alpha_2v_2} {v_2-v_1} \frac {L} {T}$

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

3. The attempt at a solution
For example with ice and water, I assume $v_2 \simeq v_1$ and then I try to solve the differential equation but I don't get to $L\simeq constant$.

2. Jan 7, 2015

Staff: Mentor

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

Chet