Consider the air in an oven at 500 K. The oven has a volume of
0.15 m^3 and contains 2.2 × 10^24 identical nitrogen molecules, each
having five degrees of freedom and a mass of 4.8 × 10^−26 kg. (a)
What is the thermal energy of this system? (b) The magnitude of the
momentum of any molecule can range from 0 to p0. Estimating p0 to
be roughly twice the root mean square momentum, what is the volume
in momentum space that is available to any particle? (c) We are
going to calculate the number of accessible quantum states for the
molecules' translational motions, ignoring the rotational states
because the latter turn out to be relatively few in comparison.
Considering the translational motion only, how many different
quantum states would be accessible to any particle, if it were all
by itself? (VrVp/h^3, where Vp = (4/3)πp^3/0.) (d) What is the number
of states per particle ωc corrected for the case of identical
particles? (e) How many different quantum states are accessible to
the entire system?