Re: [Phys-L] phase change

["Daniel V. Schroeder" <dschroeder@weber.edu>]

Carl, I don't think you'll find a purely mechanical answer to your first question.  Phase equilibrium is a thermodynamic state in which particles are constantly moving back and forth between the two phases.  One way to define equilibrium is to say that the rates of sublimation and condensation are in balance.  The temperature of a phase transformation is precise only if we hold the pressure fixed and only in the thermodynamic limit, as the number of particles goes to infinity.  In the thermodynamic limit, a slightly higher temperature (at the same pressure) makes sublimation occur more quickly and condensation occur more slowly, so any remaining solid sublimates until a new all-gas equilibrium is reached.  Similarly, a slightly lower temperature (at the same pressure) makes condensation occur more quickly and sublimation more slowly, so all the gas condenses.  There's only one temperature (at a given pressure, and neglecting finite-size effects) at which the sublimation and condensation rates are in balance.

Dan


> From: Carl Mungan <mungan@usna.edu>
> Subject: [Phys-L] phase change
> Date: February 23, 2016 2:27:36 PM MST
> To: PHYS-L <phys-l@phys-l.org>
>
>
> Okay, I’m confused about a really basic point of thermodynamics. I’m looking for answers that I can use in my introductory class.
>
> Consider a simple model of a monatomic solid, say copper, that makes a phase transition to a simple fluid (call it a gas and let’s not worry about liquids to keep things simple). So we’ll say it sublimates (but call it melting if you prefer).
>
> Here come my questions:
>
> 1. Why is there a definite sublimation temperature T?
>
> Possible answer: We’ve got a Morse potential. The temperature T corresponds to the dissociation energy E divided by the Boltzmann constant k. (I won’t quibble about whether we should measure E relative to the bottom of the well or relative to the ground state energy.)
>
> 2. Okay, so why doesn’t the temperature change while the material sublimates?
>
> Textbook answer: Temperature measures average kinetic energy KE. During the phase change the KE doesn’t change; only the potential energy PE changes as we break bonds.
>
> Say what? Even ignoring the fact that the Dulong-Petit model is obviously saying the vibrational PE is also proportional to temperature, this answer still doesn’t make sense. If a molecule just manages to dissociate, it would break free of the bond with very low KE. Why ever would one say the KE doesn’t change if we look at the Morse potential?
>
> Attempt to improve on the answer: Instead consider a model of particles in a box. In the solid phase, the box is narrow. We then adiabatically make the box wider to correspond to the lower density of the fluid phase. By “adiabatically" I here mean we keep the particles on average in the same energy levels as we move the walls of the box outward. It takes energy (I’m assuming there’s some kind of externalpressure on the walls so they don’t spontaneously fly apart) to move these walls, but the average energy level doesn’t change and so neither does the temperature.
>
> Now the new problem is I can no longer answer question 1 in this model. Why should the walls start to move at some specific T?
>
> Okay, so there we are. Help me out. Try to keep your answers at the same simple level of the ideas I’m using here. And by the way, what do you think of the animation of the two black molecules in the ice and surrounding water about halfway down the following webpage?
>
> http://zonalandeducation.com/mstm/physics/mechanics/energy/heatAndTemperature/changesOfPhase/changeOfState.html 
>
> -----
> Carl E Mungan, Assoc Prof of Physics  410-293-6680 (O) -3729 (F)
> Naval Academy Stop 9b, 572C Holloway Rd, Annapolis MD 21402-1363 
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