Maxwell Boltzmann Speed Distribution

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SUMMARY

The discussion centers on the Maxwell Boltzmann speed distribution in one-dimensional gas systems, specifically examining the relationship between Vmost probable, Vaverage, and Vrms. It is established that in a one-dimensional scenario, these three quantities are equal to each other, as they all converge at the peak of the Gaussian curve representing the distribution. The definition of root mean square velocity (Vrms) is clarified, emphasizing its calculation as the square root of the average of the squares of the velocities.

PREREQUISITES
  • Understanding of Maxwell Boltzmann distribution
  • Familiarity with Gaussian curves
  • Knowledge of statistical mechanics
  • Basic mathematical skills for calculating averages and square roots
NEXT STEPS
  • Study the derivation of the Maxwell Boltzmann distribution in three dimensions
  • Learn about the implications of Vmost probable, Vaverage, and Vrms in thermodynamics
  • Explore the mathematical formulation of root mean square velocity
  • Investigate the differences between one-dimensional and three-dimensional gas behavior
USEFUL FOR

Students of physics, particularly those studying thermodynamics and statistical mechanics, as well as educators looking to explain the Maxwell Boltzmann speed distribution in various dimensions.

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Homework Statement



The three quantities Vmost probable, Vaverage, and Vrms, are not the same for the Maxwell speed distribution in 3D. If you restrict the gas to only be one dimensional, are these three quantities equal to each other? Justify your answer with a short explanation.

Homework Equations


The Attempt at a Solution


The curve looks like gaussian curve. I know Vmostprobable is going to be the peak of the curve. And Vaverage would also be at the peak of the curve which is at V=0. I am not sure how to get Vrms
 
Last edited:
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What's the definition of ##v_\text{rms}##?
 
Root mean square velocity
 
I was looking for perhaps a mathematical formula or some other indication that you know what those words mean.
 

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