N 2  has a molecular weight of 28.02 g/mol a bit larger than that of a Ne atom, 20.18 g/mol. (a) At a particular temperature, Z trans= 1.90 x 10 26 for Ne in a specific container. What is the translational partition function for a N2 molecule in this container at the same temperature? (b) At 100 K, the rotational partition function for N2is found to be 17.39. What would you expect it to be at 500 K?

the partition function of an ideal gas of diatomic molecules in an external electric field & is [g(V, T, 8)]" Q(N, V, T, 8) N! where (2mmkT 312 (87 IkT -hv/2kT e q(V,T, 8)= V{ h2 (kT' (µ8 sinh kT) h2 (1 – e-hv/kT) Here I is the moment of inertia of the molecule; v is its fundamental vibrational frequency; and u is its dipole moment. Using this partition function along with the thermodynamic relation, dA = -S dT –p dV – M de where M=Nū, where u is the average dipole moment of a molecule in the direction of the external field &, show that kT] coth kT, Sketch this result versus & from & =0 to & =∞ and interpret it.

A car tire contains 0.034m^3 of air at a gauge pressure of 2.76x10^5 N/m^2. The composition of air is about 78% nitrogen (N2) and 21% oxygen (O2), both diatomic molecules. How much more internal energy, in joules, does the air in the tire have than the same volume of air has at zero gauge pressure outside the tire? Eint,2 - Eint,1 = _____

The Z factor is approximately the same for all gases at the same reduced temperature and reduced pressure.