
#1
Nov1612, 12:32 AM

P: 1

I want to know if the Maxwell speed distribution is the following.
An ideal gas system of n particles, say constrained to the unit box, has the phase space ([0,1]^3 x R^3)^n. That is, [0,1]^3 for the position of a particle, R^3 for the velocity, and all to the n since there are n particles. Now in this space we can take the surface of constant energy say E=n/2, so that the average energy of a single particle is 1. This surface has finite surface area, so we can put a uniform probability distribution on it, and ask what the distribution of the first particle's velocity is. Is said distribution the Maxwell speed distribution, in the limit as n>infinity? In other words, is the Maxwell speed distribution just the distribution for the velocity of a particle found in a system chosen uniformly over all systems of the same energy E? Thanks in advance! 



#2
Nov1612, 08:15 AM

Mentor
P: 10,854

The usual derivation assumes that the particles are in contact with some external reservoir and that the total energy can vary a bit. In the limit of infinite particles, I would expect that an exact energy gives the correct result, too.



Register to reply 
Related Discussions  
Maxwell speed distribution  Advanced Physics Homework  2  
Maxwell Speed Distribution  Advanced Physics Homework  11  
The Maxwell Speed Distribution in 2D  Advanced Physics Homework  2  
maxwell's speed distribution law  Advanced Physics Homework  4  
energy distribution and Maxwell speed distribution  Advanced Physics Homework  5 