The gas of oxygen at temperature 100 °C can be treated as ideal gas. (a)What is the internal energy of the gas? (b) what is the average translational kinetic energy for each of the oxygen molecule? (Consider Oxygen as diatomic molecule structure which consists of translational and rotational degree of freedom only. No vibration motion is considered) Boltzmann constant is kg = 1.38 × 10-23J/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.

[11] An experimental balloon contains hydrogen gas (H2) at a temperature of 300 K and a pressure of 1 atm (1.01 X 10° N / m?). (a) Calculate the mean-free path of a hydrogen molecule. Assume that a H2 molecule is effectively spherical, with a mean diameter of 1.6 X 1010 m. (b) Calculate the available volume per molecule (VI N), and find the average distance between each molecule and its nearest neighboring molecule (approximately the cube root of the available volume). Which is larger, the mean free path or the average nearest-neighbor distance between molecules? Exploring relationships