FiG. 4.16. Band absorptance as a function of CO2 amount (g cm~2) for the 15 ¡m bands, depicting the linear, square root and logarithmic limits at effective broadening pressures of 1.0 and 0.001 atmospheres, at T = 300 K.
equilibrium, we can write the ratio of the population n\ of the lower vibrational-rotational level and the total population, n, of the molecule in terms of the Boltzmann distribution where, Ev is the energy of the lower vibrational level v, there is no degeneracy associated with v, while gJ and Ej are the degeneracy and energy associated with the lower rotational level, J, of the transition, while Qv and Qr are the partition functions for vibration and rotation, respectively. We have assumed that vibration and rotation do not interact, a good approximation for the lower vibrational levels that are of atmospheric interest, and so the total partition function for vibration-rotation, Q(T) = QvQr, the product of the individual partition functions. The rotational partition function for diatomic and linear polyatomic molecules, considered as a rigid rotator, can be written as
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