According to Maxwell’s Distribution Law, in a gas of molecular mass m, the speed v of a molecule in a gas at temperature T (kelvins) is a random variable with density

where k is Boltzmann’s constant. Show that the average molecular speed is equal to (8kT/πm)^1/2. The average speed of oxygen molecules at room temperature is around 450 m/s.

Transcribed Image Text:

m 3/2 2лkТ p(v) = 4( v² e-mv²/(2T) (v≥ 0)