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] App. for Was: Re: T dS versus dQ



The collisions between the gas molecules and the moving piston are exactly what end up giving the adiabatic ideal gas relationships - like P V^gamma = constant, etc. If an analysis doesn't give this result something is incorrect. One thing that bothers me here is that only the component of velocity in the direction of the piston motion should be changed by 2v, not the entire magnitude of the speed. Perhaps this is why the anomalous high temperatures are resulting.

Bob at PC



-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of John Mallinckrodt
Sent: Wednesday, February 10, 2010 2:41 AM
To: Forum for Physics Educators
Subject: Re: [Phys-l] App. for Was: Re: T dS versus dQ

Bob LaMontagne wrote:

it would be nice for the smiling professor to be able to give a
ballpark estimate of how large the temperature difference is
between slow and rapid adiabatic compression for specific instances
(say mach 0.0001 versus mach 0.9).

Okay. I'll give it a very rough, back-of-the-envelope go, but no
guarantees!

I figure that if you compress a monatomic gas to half its volume in a
rigid container using a rigid piston moving at the sound speed,
you'll hit something like half of the gas molecules one time and give
them something like two to three times their original speed on
average. (I have in mind an average molecule that is moving
generally toward the piston but at, say, a 45 degree angle in the lab
frame and having an initial velocity equal to the rms speed which is
34% faster than the piston is moving. If that molecule makes an
elastic collision with the piston, I calculate that it will leave
with about 2.3 times its initial speed.)

If half the molecules have their speeds increased by a factor of 2.3
then the gas would increase its total energy--and, therefore, its
temperature by a factor of about 3. This is to be compared with an
isentropic compression that increases the temperature by 30%.

While I don't have a lot of confidence in this calculation, it seems
to me that it might not be a bad estimate for a monatomic gas having
a mean free path on the order of the cylinder length. I'm not sure
how it might need to be modified for a shorter mean free path (which
would lead to a partial thermalization of the gas during the motion
of the piston) or for a diatomic gas (which might have its
vibrational and rotational modes excited by the collisions as well.)
In any event, I'm certain that you would never actually see such a
large temperature rise simply as a result of the substantial heat
flow to the (actually non-rigid) walls that would take place with the
first round of energetic gas collisions.

John Mallinckrodt
Cal Poly Pomona
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l