Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: [Phys-L] phase change

Carl,

Sorry it took me a few days to get back to this. I'll try to respond line by line below.

From: Carl Mungan <mungan@usna.edu>
Subject: Re: [Phys-L] phase change
Date: February 25, 2016 10:32:00 AM MST
To: PHYS-L <Phys-L@Phys-L.org>


1. Do the particles in the gas and in the solid have the same (a) average kinetic energy?

Classically, yes, by the equipartition theorem. Quantum mechanically, no, unless you're reasonably close to the high-T limit where the equipartition theorem applies. At lower temperatures there's an exponential suppression of vibrational modes with hf >~ kT.

I mean for gas and solid coexisting at the sublimation point and I mean for a real material. You may pick any real material you like.

Since I don't understand the purpose of question 1(a), I don't know how I would go about picking a material. Nature, of course, provides us with a great variety of materials. Some solids are more or less classical (in this sense) at room temperature, while others aren't.


(b) average total energy?

Absolutely not. The average potential energy per particle in the solid is negative, compared to the gas.

So equipartition doesn’t apply?
To be more fair, are there two kinds of PE: vibrational PE (as used in the Dulong-Petit model for instance) and binding PE (which is what I assume you’re referring to)?

As you know, equipartition applies to the vibrational energies, in the classical (high-T) limit. But the zero point for calculating the vibrational potential energies is arbitrary. The only way to make a non-arbitrary comparison between the total energy per particle in the gas and the total energy per particle in the solid is to include the binding energy as well.


Carl, I still get the impression that you're looking for a purely mechanical (rather than thermodynamic, or statistical, or kinetic) explanation here. Is that a fair statement?


I’m not sure I know what you mean. I’ll accept any thoughts or ideas that would fly in an introductory majors physics class. This is the thermo part of their first course. So anything you want to say at that level, I’m happy to go with.

Well, I would again recommend a kinetic explanation, as I tried to outline in an earlier post. The rate at which particles sublimate off the solid into the gas is a strongly increasing function of temperature, because kinetic energies increase with temperature and a particle needs a certain amount of kinetic energy to overcome the binding energy and break free. On the other hand, the rate at which particles condense from the gas onto the solid is a decreasing function of temperature if the pressure is held fixed; this is because higher T means faster particles and hence more momentum from each collision, and so the collisions must occur less frequently (due to lower density). So if you plot the increasing sublimation rate and the decreasing condensation rate as functions of temperature, the lines must cross at some precise T. That's the equilbrium temperature.


-----
Carl E Mungan, Assoc Prof of Physics 410-293-6680 (O) -3729 (F)
Naval Academy Stop 9b, 572C Holloway Rd, Annapolis MD 21402-1363
mailto:mungan@usna.edu http://usna.edu/Users/physics/mungan/