Saturday, February 13, 2010

Adiabatic cooling puzzle

I'm a big fan of the PhET simulations.

But I'm puzzled by one aspect of the "Gas Properties" simulation.

If you open the simulation and squirt some gas (maybe 100 particles) into the chamber, the particles bounce around nicely. If you then compress the gas, the pressure and temperature increase as one might expect.

But reset it, squirt some gas in, and expand the chamber. The pressure drops, but the temperature remains the same. I was hoping for adiabatic cooling, but all I got was isothermal (and adiabatic!) expansion.

My thoughts? I want the temperature to drop: particles bouncing off a receding wall should recoil with reduced speed. And an expansion shouldn't be isothermal unless heat is added.

The good people at PhET assure me this is what's supposed to happen. But sometimes I'm just too thick to get it.

Educate me, experts!


James said...

Thermo's not my first love either, but a thought.
T prop. to KE.
No reason why KE should decrease When Volume goes up.

Kenneth Finnegan said...

What you expect is correct, and their simulation does as such. The problem is that as you make the space smaller, all of the particles in dV are impacted by the moving wall, and gain energy. As you make the space bigger, only the particles which happen to be striking the left wall lose energy, so the isothermal expansion you see is an artifact of statistical mechanics. Run the same simulation with a couple moles, or expand and contract it very slowly, and this problem will go away.

Anonymous said...

Well, there's bigger and there's receding. I assume that the simulation models one of those idealized slow expansions, so that the speed of the walls is taken to be zero. But... T should still change, as I see it.

Anonymous said...

i suspect a faulty simulation. might try the davis gas simulation

Paul Doherty said...

Hi Dean

You expanded the piston faster than the speed of sound in the gas (Or at least nearly supersonicaly).
I started with the piston completely compressed, added three squirts of light atoms. Expanded it at a rate such that atoms collided with the piston and it cooled nicely. Then again with heavy atoms, expanding it slowly it cooled nicely. Expanding it as rapidly as possible led to no collisions and no loss of temperature. Our usual rules do not apply to supersonic piston motion.

Dean Baird said...

Thanks, all. I'm assured this behavior is consistent with the principles of free expansion and the Joule-Thompson Effect. No sim bug!

@Paul, slow and reversible... I remember such things from my old Thermo class, now that you mention it. Years of exposure to energetic and impatient students appears to have taken its toll.

ytba said...

Whenever I expand the chamber, nothing happens at all, both T and P remain the same as before expansion. Something is definitely wrong with the applet.