Liquid molecular Velocity Distribution

In summary, the Maxwell distribution does not hold for liquids due to the presence of intermolecular forces. Progress has been made in describing the molecular velocity distribution for liquids, such as using pair distribution functions, but a satisfactory solution has not been found. The molecular velocity distribution for a liquid can be roughly approximated by m^3v^5/(kT)^3 * EXP [-mv^2/kT]. However, this is not as accurate as the Maxwell-Boltzmann distribution for gases.
  • #1
AdamPhysics
3
0
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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  • #2
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.
 
  • #3
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
 
  • #4
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.
 
  • #5
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.
 

What is liquid molecular velocity distribution?

Liquid molecular velocity distribution is a statistical representation of the velocities of molecules within a liquid. It shows the range of velocities that molecules can have at a given temperature, and the likelihood of a molecule having a certain velocity.

How is liquid molecular velocity distribution related to temperature?

Temperature plays a crucial role in liquid molecular velocity distribution. As temperature increases, the average velocity of molecules also increases, resulting in a broader distribution of velocities. This means that at higher temperatures, there is a greater chance of molecules having higher velocities.

What factors affect liquid molecular velocity distribution?

The main factors that affect liquid molecular velocity distribution are temperature, molecular mass, and intermolecular forces. As mentioned before, temperature influences the average velocity of molecules. Molecular mass affects the range of velocities, with lighter molecules having higher velocities on average. Intermolecular forces, such as hydrogen bonding, can also impact the velocity distribution.

How is liquid molecular velocity distribution measured?

Liquid molecular velocity distribution can be measured using various techniques, such as spectroscopy, light scattering, and molecular tagging. These methods involve measuring the velocities of a large number of molecules and then creating a distribution curve.

What is the significance of liquid molecular velocity distribution?

Understanding liquid molecular velocity distribution is crucial for studying the behavior of liquids, such as diffusion, viscosity, and heat transfer. It also has practical applications in fields such as engineering, chemistry, and biology, where the movement of molecules plays a critical role.

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