Partition Function for Monatomic Gases

Internal Partition Function for Monatomic Gases.—For the present purpose, for the internal energy of a monatomic gas only the nuclear spin and electronic states need be considered. On the assumption that these energies are additive, the partition function can again be factored  

The nuclear spin partition function is given by (2i + 1) where i is the nuclear spin quantum number, since the energy of nuclear orientations is very small compared with kT Thus, for the hydrogen atom ( H), / = 1/2 and for the chlorine atom i = 3/2 giving nuclear spin contributions of 2 and 4, respectively, to the partition function. However, it is conventional to omit these factors from calculated entropies. 

Using equations (9), (10), and (11) we find that this factor in the partition function contributes to C%(X)jLk an amount 0.128 at 300 K and 0.236 at 500 K. Using equations (7) and (10) we find that the contribution at 298.15 K to S /Lk is 1.42 the translational contribution is 18.44 so the electronic contribution is about 7% of the total. The electronic contributions must always be evaluated by summation a further example may be found in reference 3. Much information on atomic states and energy levels has been critically evaluated and tabulated.  

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