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Re: [Phys-L] phase change

Suppose we have the system in a closed container with a piston maintaining constant pressure. Inside the container we have only the substance in question, part of it solid and part of it gas. a little bit of energy flows into the system due to a temperature difference. This knocks a particle out of its potential well and makes it a free particle. Assume the energy delivered to the particle is just a tiny bit more than is need it to knock it out so it has very little kinetic energy as a free particle. The average kinetic energy of the gas is lowered because one more particle has been added to the gas and that particle has less kinetic energy than the average of the others. This tends to lower the temperature of the gas. Because there are now more gas particles, the pressure would be greater if the volume did not increase. So the piston extends outward. The gas has done some work so its average kinetic energy must have decreased. This tends to lower the temperature of the gas. Assuming the particle in question to have been at the top of the set of energy levels for the solid, the solid has lost one of those particles near the surface of the solid that had a higher kinetic energy level than the average kinetic energy of a bound particle at the surface. This tends to lower the temperature of the solid. The departure of the particle from the surface has changed the potential well that its neighbors are in. They are not as strongly bound as they were. The bottom of their potential well has risen thus increasing their potential energy (making it less negative) and decreasing their kinetic energy (how far above the bottom of the well they are in) by the same amount. This tends to lower the temperature of the solid. If that were all there was to it, adding energy to the system would result in a temperature decrease.

Some of the energy that flows in through the walls of the container due to the temperature difference between the system and its surroundings will directly increase the kinetic energy of the gas molecules. This tends to increase the temperature of the gas. Some of the inflowing energy will bump molecules in the solid up to higher energy levels thus increasing their kinetic energy. This tends to increase the temperature of the solid. If that were all there was to it, adding energy to the system would result in a temperature increase.

We have competing effects. There is a tug of war. At this level of discussion, all three temperature changes (increase, decrease, stay the same) are possible. All we can say is that it is plausible that it would stay the same. The experimental result does not create a paradox.

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@www.phys-l.org] On Behalf Of Carl
Mungan
Sent: Thursday, February 25, 2016 12:32 PM
To: PHYS-L
Subject: Re: [Phys-L] phase change

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.

(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)?

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.

-----
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/

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