# Ideal Gas Law Equilibrium Requirements

Tags:
1. Jun 30, 2015

### 0pt618

It is well known that the ideal gas law applies only to an ideal gas, one consisting of particles infinitesimal in size and exhibits no interactions between the particles. Considering an ideal gas, is the ideal gas law valid under non-equilibrium conditions? For example, does the ideal gas law hold for all instants of in the free expansion of an ideal gas?

References, if available, would be appreciated.

2. Jun 30, 2015

### Kazys

"Free"expansion? How do you define volume for such a condition? PV = MRT is then not valid.
The Maxwell-Boltzman distribution is not valid either. Lets assume the expansion of a Ne
gas volume starts from an initial equilibrium state. At say 20 C the Ne atoms have an average
velocity of ~850m/s, but there are atoms with velocities close to 0 m/s and some which
move at over 2000 m/s. Clearly in a "free" expansion the velocity distribution at the boundaries of the
expanding Ne cloud will not be Maxwellian.

3. Jun 30, 2015

### 0pt618

Kazys, thank you. But why is it that "the velocity distribution at the boundaries of the gas will not be Maxwellian" in a "free" expansion?

4. Jul 2, 2015

### Kazys

My answer is simplistic, and because of that chances are that it is correct. Consider the Ne cloud before its free expansion. Within the could
the molecules interact, the probability is that fast ones loose energy, slow ones gain it. Equilibrium is maintained. At the edges the fast
molecules move faster in all directions including the outward directions. There they do not interact but keep moving. The slow ones
tag behind. Consequently the ratio of fast to slow molecules changes, thus it is no longer Maxwellian.

5. Jul 2, 2015

### 0pt618

Thanks Kazys - this makes sense. As an aside, you are referring to Occam's razor, when you say the simple answer is usually the correct one, right?