Rotational Cut-Off and Anharmonicity Effects on Thermodynamic Properties of Gases at High Temperatures

Summary The exact expressions for the partition function Q and the coefficient of specific heat at constant volume C v for a rotating-anharmonic oscillator molecule, including coupling and rotational cut-off, have been formulated and values of Q and C v have been computed in the temperature range of 100°K to 100 000°K for O 2 , N 2 and H 2 gases. The exact Q and C v values are also compared with the corresponding rigid-rotator harmonic-oscillator (infinite rotational and vibrational levels) and rigidrotator anharmonic-oscillator (infinite rotational levels) values. The rigid-rotator harmonic-oscillator approximation can be accepted for temperatures up to about 5000°K for O 2 and N 2 . Beyond these temperatures the error in C v will be significant, owing to anharmonicity and rotational cut-off effects. For H 2 , the rigid-rotator harmonic-oscillator approximation becomes unacceptable even for temperatures as low as 2000°K.