PHYS 317 - Reading Assignment #19

  1. 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.

  2. 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).

  3. 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.
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