1. Statistical Thermodynamics of the Perfect Monatomic Gas
Valentim M B Nunes
ESTT – IPT
May 2015

2. The partition function allows the calculation of the properties of a system from the knowledge of the energy levels of particles.

3. In the case of a monatomic ideal gas the only form of energy is the kinetic energy of translation. To obtain the translational energy levels we use the model of particle of mass m in a box of volume V = a  b  c. Quantum mechanics tells us that:
Where p, q and r are the translational quantum numbers, integers ranging between 1 and .

4. For each form of translation we have:

5. As the translational energy varies almost continuously, then:
Translational partition function comes:

6. Knowing the partition function we can calculate the thermodynamic properties of an assembly of N particles that behave like a perfect monatomic gas.

7. We can now calculate the pressure of a perfect gas:
Per mole, N = NA, and we obtain:

8. For the translational entropy:

9. Eliminating the volume and introducing the equation of state, we obtain, in S.I. units, the Sackur-Tetrode equation:
Not foreseen by classical thermodynamics!
Important! Allows you to calculate the absolute entropy of a monatomic gas. Ex: Argon at K, S°m = J.mol-1.K-1

11. Per system (molecule) the average kinetic energy is therefore:
Principle of equipartition of energy: each of the three quadratic modes of expression of the translational kinetic energy contributes with 1/2 kBT for energy.
This result shows that, in fact,  = 1/kBT

13. Gas Cp CV  He
20.79
12.6
1.63 Ar
12.4
1.667 Xe
1.666