The velocity of the molecules in a homogeneous gas that is in the state of equilibrium can be described by a continuous variable V with density function

for some positive constant a.

(i) Find the value of a using the following result (known from calculus):

(ii) Obtain the density function of the variable

which represents the kinetic energy of the molecules (here, m is the molecule mass, which is assumed to be known).

Transcribed Image Text:

f(v) = ve-av v > 0,