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

AI Thread Summary
The discussion focuses on demonstrating that the latent heat (L) remains approximately constant during solid to liquid transitions at temperatures much lower than the critical temperature (Tc). The relevant equation involves the specific heat capacities (cp) and the coefficients of volumetric expansion (α) for both phases. A participant attempts to solve the differential equation but struggles to derive the conclusion that L is constant. They suggest using the Clapeyron equation to relate pressure and temperature changes along the solid-liquid equilibrium line. The conversation emphasizes the need for a clearer approach to solving the problem.
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Homework Statement


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.

Homework 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.

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.

Can anybody help me please?
 
Physics news on Phys.org
Consider using the Clapyron equation which relates the changes in pressure and temperature along the equilibrium line between solid and liquid.

Chet
 

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