# Velocity of real gas molecules?

It is known that the velocity of ideal gas molecules can be computed using Maxwell-Boltzmann law of distribution of molecular velocities, with average velocity given as:

$\overline{v}=\sqrt{\frac{8RT}{\pi M}}$

What would be the corresponding velocity for a real gas (which are not at STP)? Thanks!

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At STP everyday gasses are pretty close to ideal. – dmckee♦ Nov 26 '12 at 2:58

## 1 Answer

There is an important thing to note about your question, which is the understanding the relationship between math and physics. Physics uses mathematical equations to describe reality. Physics equations are approximations and may assume certain conditions (pressure, temperature, etc.) to offer an equation that is strictly true under those certain conditions. Thus, physics equations like the one you provided has boundaries in where its true.

In order to find the average velocity for real gases, you'll need to strictly define the conditions your gas is under. Although the average velocity of gases given by Maxwell-Boltzman distribution may be accurate, it may still deviate from a real gas you are asking about because it may be under different conditions. You may need to add or subtract some term to the equation you provided in order for it to match your real gas.

In short, there is no corresponding velocity for a real gas in the sense that "no physics equation to date is perfectly accurate in describing reality."

You may have a very accurate and precise equation that corresponds to reality, but it still serves as an approximation. What's great is that depending upon the system you are studying, sometimes you don't need such a large accuracy and your physics equation may have an accuracy that may exceed the system in question. This would be the case where your physics equation would be equivalent to describing reality, but you really need to specify your system first.

Moreover, since the equation is describing an average velocity, it means that you could have a distribution of velocities that has a large spread or a small spread.

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The current model I use is already based on the assumption of no major deviation in ideal and real gas velocity. However, I want to improve on that ideal gas assumption I am using in my model to the real gas. – S_H Nov 26 '12 at 6:05
In that case, like I've stated, you'll need to find some extra term that's added or subtracted to the ideal gas law that applies to the real gas you are talking about. That extra term is currently not there and physicists don't bother to find an extra correction because the ideal gas law works pretty well already. However, this gives more reason for you to try to find it! Perhaps you'll rewrite textbooks! :D – QEntanglement Nov 30 '12 at 17:25
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