The problem is about statistical thermodynamics:

Consider N particles of ideal gas in a box of volume V and in thermal contact with a reservoir of temperature T. We will let our ideal gas particles have some internal structure and dynamics, like rotational and vibrational modes.2 Let i = 1, - - - N label the gas particles and let Emmi be the internal energy of the ith molecule (containing, for example, the rotational energy and vibrational kinetic and potential energies). Rather than studying the full gas let's focus our attention on a single molecule. Given a microstate 51, the energy is given by E()= ldl + E' , 2m int,1 where our microstate is determined by its position i (which can be any position inside our volume), its momentum 15' (with no restrictions), and its internal state Jim (which may contain information like the rotational and vibrational quantum numbers). We will also make use of the following denitions: 3/2 . . h l 21rkaT Zin E 815E111t'1('~41nt)3 A E a n E . = ( . t'l ; m x/27rmchT Q Afh h2 Note that the \"sum over microstates\" for the phase space variables ($1,131) of our rst particle becomes a phase space integral, dS-'d3v \" 2 (stuff)\" => ff] f/f(stu)%, 45:13") where the h3 is our \"unit of phase space volume.\" (a) Determine the partition function Z1 for a single particle of our ideal gas. Hint (highlight to reveal): [ 1 Answer {highlight to reveal): [ l If our N gas particles were distinguishable we would be able to use our result from Problem Set 6 and simply declare that since each of the N particles has the same l-particle partition function Z1, the total partition function would be Z = Z1\