%0 Journal Article
%T Mechanical Proof of the Maxwell Speed Distribution | Lin | International Journal of Statistics and Probability | CCSE
%A Hejie Lin
%A Tsung-Wu Lin
%J International Journal of Statistics and Probability
%D 2019
%I 
%R 10.5539/ijsp.v8n2p90
%X This article derives the probability density function ¦×(¦Î;x,x')£¿ of the resulting speed ¦Î £¿from the collision of two particles with speeds x £¿and x' . This function had been left unsolved for about 150 years. Then uses two approaches to obtain the Maxwell speed distribution: (1) Numerical iteration: using the equation£¿£¿£¿P_new(¦Î) =¡Ò_0^¡Þ ¡Ò_0^¡Þ¦×(¦Î;x,x') £¿P_old(x) £¿P_old(x') dxdx'£¿ to get the new speed distribution from the old speed distribution. Also, after 9 iterations, the distribution converges to the Maxwell speed distribution. (2) Analytical integration: using the Maxwell speed distribution as the P_old(x) , and then getting P_new(¦Î)£¿ from the above integration. The result of P_new(¦Î)£¿ from analytical integration is proved to be exactly the Maxwell speed distribution
%U http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/38323