Lecture 8 - Molecule in an Ideal Gas (Maxwells Velocity...

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1 Molecule in an Ideal Gas (Maxwell’s Velocity Distribution) One molecule—remaining ones constitute the reservoir 2 2 1 22 p E mv m  Probability 33 ( , ) P r p d r d p that the molecule has position lying in the range   , r r dr , momentum   , p p dp 2 3 3 3 3 ( /2 ) does not depend on ; can be integrated out ( , ) pm rr P r p d r d p d r d p e   3 P p d p Probability that momentum is in the range   , p p and that r could be anything     2 2 3 3 3 /2 integral over 3 and is a constant. r P p d p d r d p e V e d p V  Since v, Velocity Distribution is given by 2 3 v /2 3 (v) v v m P d e d or, 2 v /2 (v) normalization constant m P C e  Molecule in an Ideal gas in the presence of gravity 2 2 p mgz m  H We want to figure out pressure (z). As before,     2 2 2 3 3 3 3 ( ) 3 3 ( ) 3 integrate out ( , ) ( ) ( ) same as before p m mgz mgz P r p d r d p d r d p e P p d p d r e d p e P p d p C e d p 
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This note was uploaded on 09/28/2011 for the course PHYSICS 971 taught by Professor Chakabarti during the Spring '10 term at Kansas State University.

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Lecture 8 - Molecule in an Ideal Gas (Maxwells Velocity...

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