- #1
weezy
- 92
- 5
Maxwellian velocity distribution is obtained by $$g(v_x)\propto e^{-mv_x^2/2k_B T}$$ and when extended to 3 dimensions the distribution becomes: $$\propto e^{-mv_x^2/2k_B T}e^{-mv_y^2/2k_B T}e^{-mv_z^2/2k_B T} = e^{-mv^2/2k_B T}$$
Now looking at the speed distribution we take a spherical shell in phase space between ##v , v+dv## and obtain: ##f(v)dv \propto 4\pi v^2 dv e^{-mv^2/2k_B T}##
My question is that are the two distributions equivalent since ##f(v)## has a extra ##v^2## term but logically the two seem equivalent?
Now looking at the speed distribution we take a spherical shell in phase space between ##v , v+dv## and obtain: ##f(v)dv \propto 4\pi v^2 dv e^{-mv^2/2k_B T}##
My question is that are the two distributions equivalent since ##f(v)## has a extra ##v^2## term but logically the two seem equivalent?