Phase cells and equilibrium speed distribution

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SUMMARY

The discussion centers on determining the equilibrium distribution of molecular speeds in a pure gas, given the probability of molecules occupying phase cells. It is established that the atomic mass of the molecule is essential for calculating speed distribution. Additionally, the absolute temperature is required when using the speed distribution function f(v) = Bv² e^(-mv²/2kT). Participants emphasize the importance of understanding the components of the equation to derive the necessary information for accurate calculations.

PREREQUISITES
  • Understanding of phase cells in statistical mechanics
  • Familiarity with the speed distribution function f(v)
  • Knowledge of atomic mass and its significance in molecular speed calculations
  • Basic principles of thermodynamics, particularly the concept of absolute temperature
NEXT STEPS
  • Research the derivation and application of the Maxwell-Boltzmann speed distribution
  • Study the relationship between temperature and molecular speed in gases
  • Explore the implications of atomic mass on molecular behavior in statistical mechanics
  • Learn about phase space and its role in understanding molecular distributions
USEFUL FOR

This discussion is beneficial for students studying thermodynamics, physicists interested in statistical mechanics, and anyone seeking to understand molecular speed distributions in gases.

michelle001
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Homework Statement


If the probability of any given molecule occupying any given phase cell is known, what additional information is required in order to work out the equilibrium distribution of molecular speeds in a pure gas?

Homework Equations



The Attempt at a Solution


Since the phase cells describe the position and velocity of each molecule - the speed of every molecule can be determined so long as the atomic mass is know. Since we know all phase cells we know number of molecules and the probability of each and can find the spread of speeds. So the only additional information required from that supplied in the question is the atomic mass of the molecule

I can't actually find any information to support this but having tried to figure it out and reread books for last two hours I thought I'd try my first post! can anyone help me??

or having had another think am I supposed to use f(v)=Bv^2 . e^(-mv^2/2kT) in which case I'd need the absolute temperature and atomic mass of neon?

thanks
 
Last edited:
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Hi Michelle
I'm not an expert, but I think we're doing the same course.

If you look at the equation that you stated for the speed distribution function f(v), you need to work out what the different parts of it relate to. e^-mv^2/2kT corresponds to the probability of a molecule being found in a given phase cell, so have a think about what other items of information are needed to find f(v).
Hope that helps
 

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