445lec18 - PHYS 445 Lecture 18 - Maxwell-Boltzmann...

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PHYS 445 Lecture 18 - Maxwell-Boltzmann distribution 18 - 1 © 2001 by David Boal, Simon Fraser University. All rights reserved; further resale or copying is strictly prohibited. Lecture 18 - Maxwell-Boltzmann distribution What's Important: mean speeds molecular flux Text : Reif Mean speeds The Maxwell-Boltzmann speed distribution that was derived in the previous lecture has the appearance where F ( v ) dv is the number of particles per unit volume with a speed between v and v + dv . Now, there are three common measures of the velocity distribution v 2 1/2 v rms ( root mean squarespeed ) v ( mean speed ) ˜ v ( most likely speed ) . These quantities are straightforward to calculate, and the details can be found in Reif. Root mean square One can work through the integral of F ( v ) to obtain v rms , or just invoke the equipartition theorem in three dimensions: 3 2 k B T = [ mean kineticenergy ] = 1 2 mv 2 or v rms = 3 k B T m . (18.1) Mean Evaluate the integral v = 1 n v F ( v ) dv = 8 π k B T m 0 (18.2) Most likely Determine the derivative dF ( v ) dv = 0 ˜ v = 2 k B T m (18.3) 0 v F ( v )
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445lec18 - PHYS 445 Lecture 18 - Maxwell-Boltzmann...

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