Consider a gas of particles consisting of only one species and characterized by the Maxwell-Boltzmann equilibrium distribution function (with u = 0)

(a) Show that the total number of particles crossing a unit area per unit time, lying within an element dΩ of solid angle, is given by

where θ denotes the angle between the solid angle orientation and the direction of the normal to the area considered.

(b) Show that the fraction of particles that cross a unit area perpendicular to the x axis per unit time, from the same side, having the velocity components in the range d³v = dv_x dv_y dv_z, about v, is given by

(c) Calculate the thermal energy flux triad for the Maxwellian gas.

Transcribed Image Text:

m = ( 27 ) f(v) = no 3/2 exp mv2. 2kТ