# Energy in phase transitions

bmrick
Sorry for such a simple question but where do we model the energy going during phase transitions? If I had a mercury thermometer in a pot of water, and I had a 200 degree Celsius heat reservoir in contact with the water, I would see the water temp hold steady during the phase transition, despite the fact that the kinetic model of heat implies there is still an energy transfer goin on. Am I right to think that this energy is being used in the process of displacing air as the waters volume increase and it becomes steam? What if the water was held at a fixed volume, would I still see an energy absorbent phase change?

I'm thinking this has something to do with degrees of freedom but that explanation is giving me some headaches so I thought I'd ask you bright folks

## Answers and Replies

bmrick
Enthalpy is a measure of internal energy plus the energy required to displace the local gas at its current pressure, right? So then if the volume of water is fixed will all energy go straight into internal motion and thus heat?

You say the energy also goes into breaking internal bonds, this makes sense. I do hate to be a stickler, but I'm actually trying to investigate the historical growth of thermal physics. Is there any way to explain this phenomena without the charged atomic model?

bmrick
As far as breaking bonds, I'm thinking we would say some energy went into giving two particles experiencing attraction an escape velocity. Is this accurate?

ZealScience
Is there any way to explain this phenomena without the charged atomic model?
Something like that is called a first order phase transition. If you are considering a completely ideal gas, there is only one phase after all. You would not even get a transition from the perspective of free energies and in fact no second order phase transition either. Therefore it is meaningless to discuss 'phase transition of ideal gas'.

bmrick
But day to day evidence is very clear about the existence of phase transitions. The serious divergence from expected" ideal" behavior must necessarily have been a serious pickle for physicists before they had developed the electromagnetic atom, or even proven the atom in general. I'm wondering how they mathematically made sense of it. I'm not all too familiar with Gibbs free energy, but I'll look into it and see if it is sensible without the statistical mechanical definition of entropy.

ZealScience
No, they do not simply use electromagnetism, and they are not expecting ideal gas for all substances. For example, they do not use ideal gas to model liquids. Ways to approximate include most notably Van der Waal's equation, which include first order and second order phase transition. Or there is Virial expansion which deals with any kind of interaction exactly, but impossible to integrate.

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As far as breaking bonds, I'm thinking we would say some energy went into giving two particles experiencing attraction an escape velocity. Is this accurate?

It's accurate enough, yes. In order to turn liquid water into water vapor you have to put in enough energy to overcome the hydrogen bonds and "break free". Since the molecules aren't flying off into free space escape velocity doesn't exactly apply, but it's a similar idea.

bmrick
No, they do not simply use electromagnetism, and they are not expecting ideal gas for all substances. For example, they do not use ideal gas to model liquids. Ways to approximate include most notably Van der Waal's equation, which include first order and second order phase transition. Or there is Virial expansion which deals with any kind of interaction exactly, but impossible to integrate.

In aware they didn't expect everything to hold to the ideal gas law, but wastage ideal gas law the general relationship they assumed existed between p,v,n, and T? I should look at van Der walls though, as I understand his equation corrects the ideal gas law to some extent, right?

bmrick
It's accurate enough, yes. In order to turn liquid water into water vapor you have to put in enough energy to overcome the hydrogen bonds and "break free". Since the molecules aren't flying off into free space escape velocity doesn't exactly apply, but it's a similar idea.

Yes yes but I think we're on the same page. I mean to say that while enough energy isn't given to any particle to escape the general system, it is given enough to ensure more energy is stored statistically into potential systems than before the phase change

ZealScience
In aware they didn't expect everything to hold to the ideal gas law, but wastage ideal gas law the general relationship they assumed existed between p,v,n, and T? I should look at van Der walls though, as I understand his equation corrects the ideal gas law to some extent, right?
In fact, the Van der Waals equation and Virial expansion have corrections in powers of inverse volume. This means that ideal gas law always holds for very dilute gases. But dilution means weak interaction, and also means being far from phase transition (here I am referring to liquid gas phase transitions, chemical ones are more complicated).

bmrick
So then, is van Der walls great triumph that he successfully modeled data on a continuous curve and organized the variables in an intelligible way?

ZealScience
So then, is van Der walls great triumph that he successfully modeled data on a continuous curve and organized the variables in an intelligible way?
I don't think so. His modifications were based on some physical arguments. Well, firstly it goes to ideal gas in the dilute limit, which is experimentally observed; secondly, it has theoretical phase transition and critical points, which sounds more realistic. But in many circumstances, it is still a very crude model.

Anyway, the more important point is that even without any data fitting we know that ideal gas is definitely going to fail near transition point because there is none at all!

ZealScience
By the way, the equations of states (Ideal gas and VdW are examples of them) are usually obtained from Helmholtz free energy, which could be calculated from the partition function. (If you have not done any statistical physics, just take it as a fact maybe?) Partition function is related to the energetics of the particles.

Ideal gas equation is a result of non-interacting particles (apart from collisions of course). If it fails near transition point, it means the free particle model is not working and you need to use equation of states that has phase transitions which necessarily has potential energy involved.

bmrick
Alright, I think I'm just going to have to let this go for now. It amazes me just how far we've come and how we've managed to develop such complicated models. It reminds me of how newb I am. Thanks for the help guys. Would any of you have a history of thermal physics text or online guide you might recommend?