Liquid molecular Velocity Distribution

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Discussion Overview

The discussion revolves around the applicability of the Maxwell-Boltzmann distribution to liquids, particularly in relation to molecular velocity distribution and the effects of intermolecular forces. Participants explore the limitations of the Maxwell distribution in the context of various liquids such as water, benzene, and toluene.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether the Maxwell-Boltzmann distribution applies to liquids, noting the influence of intermolecular forces like van der Waals forces.
  • Another participant suggests that the Maxwell distribution is suitable for non-interacting particles and mentions that there may be limited progress in understanding liquid interactions, particularly for strongly interacting molecules like water.
  • A participant references a 1946 publication discussing a general kinetic theory of liquids and molecular distribution functions, indicating a historical perspective on the topic.
  • One participant proposes a rough approximation for the molecular velocity distribution in liquids, although they caution that it is not as accurate as the Maxwell-Boltzmann distribution for gases.
  • A subsequent post corrects an earlier claim about the energy distribution, indicating uncertainty in the accuracy of the proposed equations.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the applicability of the Maxwell-Boltzmann distribution to liquids, and multiple competing views regarding the understanding of molecular interactions in liquids remain evident throughout the discussion.

Contextual Notes

Limitations include the potential inapplicability of the Maxwell distribution to liquids due to intermolecular forces, and the lack of intuitive models for describing liquid molecular interactions. The discussion also highlights the historical context of research on this topic.

AdamPhysics
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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.
 
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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
 
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.
 
FireBones said:
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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