- Why isn't the distribution function D(v) just equal to the
Boltzmann factor?
The Boltzmann factor tells you the probability of finding the particle in
a given state with velocity v. But many such states have the same
speed v = |v|. Thus the Boltzmann factor gets multiplied by a
term measuring the number of states as a function of v.
- If you double the temperature of an ideal gas, by how what factor
does the average speed increase?
average v is proportional to sqrt(T), so doubling the temperature increases
the average speed by a factor of sqrt(2).
- What is the most probable speed of nitrogen molecules at
room temperature?
Most probable speed (different from root-mean-square velocity and
average speed) is given by sqrt(2kT/m). For N2 this works out
to be 422 m/s.