# Gibbs free energy and melting

1. Feb 5, 2013

### AbsoluteZer0

Hi,

As I understand, during the process of phase change from a liquid to solid (or any phase change for that matter,) the temperature of the substance remains constant as the energy being applied to the substance is used in changing phase.

How does this relate to Gibbs free energy? I read that $\Delta G$ during melting is zero. Enthalpy and entropy, however, increase. Does this have any relation to the uniformity of the temperature of the substance during the change of phase?

I'm led to believe that $\Delta G > 0$ when phase change isn't taking place because of the changing temperature. (For example, when the temperature of water is raised from 30°C to 50°C.) How accurate is this assumption?

Thanks,

Last edited: Feb 5, 2013
2. Feb 8, 2013

### sankalpmittal

Gibbs free energy is not constant during phase change! Who told you this ?

Clearly ΔG=ΔH-TΔS

Entropy factor also changes though...

3. Feb 8, 2013

### DrDu

During a reversible phase change, e.g. slow melting of ice, G does not change.
$dG=VdP-SdT+\mu_l dN_l +\mu_s dN_S.$
P and T are constant and $dN_l=-dN_s$. $\mu_l=\mu_s$ is the condition for equilibrium of the two phases, so dG=0.
ΔH is positive for melting (endothemal process), ΔS, too, as the entropy of the liquid is higher than that of the solid.

4. Feb 8, 2013

### Andy Resnick

The sign of ΔG tells you if the process is spontaneous (ΔG < 0) or not. As for phase transitions, there are at least 2 kinds: a 'first order phase transition' is accompanied by a discontinuous change in the derivative of the free energy and are associated with freezing/melting/etc. ΔG = 0 for a first order phase transition (ΔH = TΔS).

Second-order phase transitions are associated with discontinuous changes to the second derivative of the free energy. IIRC, ΔG = 0 for a second order phase transition as well.

http://www.helsinki.fi/~serimaa/soft-luento/soft-2-phase.html

5. Feb 12, 2013

Thanks