Equation of State and Thermodynamic Properties of Gases at High Temperatures. I. Diatomic Molecules

Abstract

Methods for evaluating the thermodynamic properties of assemblies of chemically reacting unionized atoms are discussed. The desirability of using the virial coefficients at high temperatures instead of the customary use of the molecular partition functions with anharmonicity corrections is emphasized. The most realistic three‐parameter diatomic potential energy function that is available at present, i.e., the Rydberg potential, ${\mathrm{U/U}}_e{\text{=−(1+b}}^{\prime }\mathrm{\xi )\hspace{0.17em}}\exp {\mathrm{(-b}}^{\prime }\mathrm{\xi )\hspace{0.17em}}\mathrm{with}{\mathrm{\hspace{0.17em}\xi =(r/r}}_e\text{)−1}$ is selected for the evaluation of the classical second virial coefficient. B(T), T(dB/dT) and T²(d²B/dT²) are obtained as linear combinations involving the five functions: $$A_k\mathrm{(\theta )=}{\displaystyle \sum _{\text{n=1}}^{\infty }}{\mathrm{[(\theta e)}}^n{\mathrm{/n}}^{\mathrm{n+k}}\mathrm{],}$$ [k= —1, 0, 1, 2, and 3, and θ=(U_e/kT)] with only the coefficients that multiply A_k depending on b′. A_k is tabulated for 0.05≤θ≤10. A simple expression for estimating the quantum correction to B(T) is given. The inclusion of the contribution of the higher diatomic electronic states to B(T) is considered. The treatment is applied to sodium (including the ³Σ repulsive state), and B(T) and thermodynamic properties calculated at two temperatures by several methods are compared.