Blundell Thermal Physics · Problem 37.7

Earth's atmosphere

Physics — Statistical Mechanics · molecular-flux-irradiance

Problem

In the kinetic theory of gases it is possible to define a quantity

I = n\langle v\rangle/4\pi

as the number of molecules per second striking unit area per steradian of solid angle, where

n

is the number of molecules per unit volume and

\langle v\rangle

is the mean speed. Note that

I

does not depend on direction. Show that the flux

\Phi

of molecules is given by

\Phi = \int I \cos\theta\,\mathrm{d}\Omega = \tfrac{1}{4}n\langle v\rangle, \tag{37.37}

as in eqn 7.6, and relate this to eqn 37.20.