Ideal Gas Law Equilibrium Requirements

In summary, the ideal gas law only applies to ideal gases with infinitesimal particles and no interactions between them. It is not valid under non-equilibrium conditions, such as in the free expansion of an ideal gas. This is because the velocity distribution at the boundaries of the gas will not be Maxwellian due to the lack of interactions. This is also known as Occam's razor, where the simplest answer is usually the correct one. References, if available, would be appreciated.
  • #1
0pt618
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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.
 
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  • #2
"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. Let's 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.
 
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  • #3
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
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
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?
 

FAQ: Ideal Gas Law Equilibrium Requirements

1. What is the Ideal Gas Law?

The Ideal Gas Law is a mathematical equation that describes the behavior of an ideal gas. It relates the pressure, volume, temperature, and number of moles of a gas in a closed system.

2. What are the requirements for equilibrium in an ideal gas?

The requirements for equilibrium in an ideal gas are constant temperature, pressure, and volume. This means that there is no net change in the overall system and the gas particles are evenly distributed throughout the container.

3. How does the Ideal Gas Law relate to equilibrium?

The Ideal Gas Law is used to calculate the equilibrium conditions of an ideal gas. By manipulating the equation, one can determine the pressure, volume, or temperature needed for the gas to reach equilibrium.

4. What is the significance of the Ideal Gas Law in chemistry?

The Ideal Gas Law is a fundamental equation in chemistry that helps us understand and predict the behavior of gases. It is used in a variety of applications, such as determining the volume of a gas at a certain pressure and temperature or calculating the number of moles of a gas in a given volume.

5. Are there any limitations to the Ideal Gas Law?

Yes, the Ideal Gas Law is only applicable to ideal gases, which are hypothetical gases that do not exist in real life. Real gases deviate from ideal behavior at high pressures and low temperatures, so the Ideal Gas Law may not accurately predict their behavior under these conditions.

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