Maxwell Boltzmann Speed Distribution

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Homework Help Overview

The discussion revolves around the Maxwell-Boltzmann speed distribution, specifically examining the relationship between the most probable speed, average speed, and root mean square speed in one-dimensional gas behavior.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the equality of Vmost probable, Vaverage, and Vrms in a one-dimensional context, with one participant noting the Gaussian nature of the distribution. Questions arise regarding the definition and calculation of Vrms.

Discussion Status

The discussion is ongoing, with participants seeking clarification on definitions and relationships between the quantities involved. Some guidance has been offered regarding the nature of the speed distribution, but no consensus has been reached.

Contextual Notes

Participants are encouraged to justify their answers and provide mathematical formulations, indicating a focus on understanding rather than simply providing answers.

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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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