Liquid molecular Velocity Distribution

Main Question or Discussion Point

Does Maxwell Boltzmann hold for liquids? In the case of gases it does quite well for calculating the velocity distribution given a temperature. However, when the molecules are closer together in the case of liquids, how do the van der waals force and others effect the velocity distribution.

What are the limitations on the maxwell distribution? What can be done for the case of liquid water? liquid benzene, toluene?

Thanks in advance.
 

Answers and Replies

Andy Resnick
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The Maxwell distribution holds for non-interacting particles, like a gas. As you point out, there are intermolecular forces in liquids (and solids). I don't know how much progress has been made. I suspect more work has been done on weakly interacting molecules- which is not water. What I have seen in liquids are things like "pair distribution functions" to describe the structure of a liquid, but nothing intuitive or satisfying.
 
Thanks, for the help. I have done an extensive search and nothing seems to be out there on calculating the liquid interactions.

Found this publication from 1946

Proceedings of the Royal Society of London. Series A, Containing Papers of a mathematical and Physical Character
Vol. 188
Issue 1012
December 1946
Pages 10-18

Author: M. Born and H.S. Green
Title: A General Kinetic Theory of Liquids. 1. The Molecular Distribution Functions
 
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The molecular velocity distribution for a liquid should be (roughly) approximated by m^3v^5/(kT)^3 * EXP [-mv^2/kT]

The energy distribution is a lot "prettier" optically:
4E^2/(kT)^3 * EXP [-2E/kT]

Not sure if it satisfies your needs or not. This is not as accurate as the m-b distribution is for gases.
 
103
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The energy distribution is a lot "prettier" optically:
4E^2/(kT)^3 * EXP [-2E/kT]
Oops, when I translated into energy I made an error...and after rectifying it, it no longer looked particularly clean...so just ignore that half.
 

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