A two-dimensional gas, consisting of only one species and whose particles are restricted to move in a plane (the z = 0 plane), is characterized by a homogeneous, isotropic, two-dimensional Maxwell-Boltzmann distribution function (with u = 0),

where n₀ represents the number of particles per unit area.

(a) Show that the most probable speed of the particles is

(b) Show that the fraction of the number of particles per unit area, which have speeds greater than the most probable speed, is given by (1/e)^1/2, where e is the base of natural logarithms.

(c) Show that the number of particles crossing a unit length per unit time (flux), from one side only, is given by

(d) Show that the kinetic pressure dyad is given by

Transcribed Image Text:

m f(v) = no 0 (2TKT) exp[- m(v² + v²). 2kT