# Phase transition and Entropy

I know that in a phase transition, for example, to change from phase 1 to phase 2 at a constant temperature $$T_c$$, we need to supply some extra heat -- latent heat -- $$L = \Delta Q_R = T_c (S_2-S_1)$$.

However, a phase transition it is also associated with a change of the potential energy of the molecules. I don't see how this parameter is included in the equation for latent heat.

Could someone explain me what is missing in my reasoning?

• When latent heat is released energy must still be conserved. Where do you think the energy came from? – By Symmetry Dec 24 '20 at 11:03
• @BySymmetry Indeed as stated in the 1st law of thermodynamics. What I don't understand is how a change in entropy of the gas reflects the whole change in the potential energy of the molecules in a case of a gas for example? – JoseAf Dec 24 '20 at 16:29
• I have updated my answer after seeing your last comment to BySymmetry. Hope it helps. – Bob D Dec 24 '20 at 18:31

However, a phase transition it is also associated with a change of the potential energy of the molecules. I don't see how this parameter is included in the equation for latent heat.

The total internal energy of the substance is the sum of its molecular kinetic and potential energies. Since the temperature of the substance during the phase transition is constant, and temperature is a measure of the kinetic energy component of the internal energy of the substance, there is no change in the kinetic energy component of the internal energy of the substance during the phase transition.

Given the above, the heat transfer during the phase transition has to equal the change in the molecular potential energy component of the internal energy. Where else would the energy go or come from?

What I don't understand is how a change in entropy of the gas reflects the whole change in the potential energy of the molecules in a case of a gas for example?

This is in response to your above comment.

The increase in molecular potential energy during a phase change from a liquid to a gas results in the gas occupying a greater volume than the liquid. Gas molecules move more freely and are more "spread out" than in a liquid. Therefore the molecules have more room and more positions in which they can potentially be arranged. The more positions or microstates that can be occupied, the greater the entropy.

Hope this helps.

• B Thanks a lot for the answer – JoseAf Dec 24 '20 at 22:10

In a ideal gas, the internal energy is translational kinetic energy of the molecules, and the temperature is a function of that energy.

In a liquid or solid, it is better to think of the molecules linked as oscillators, where increasing the energy implies increasing both potential and kinetic energy.

What happens at phase transition is a change on the 3-D structure of the oscillators. It is as the former structure can not support the increased restoring force for higher energy and, so too speak, "breaks". It is the case of a transition of solid to liquid.

The new structure is not necessarily less compact. Water for exemple contracts when melting. The same happens to the solid-solid transition $$\alpha$$-iron to $$\gamma$$-iron.