Ni gj exp Ej EvkT nQvQr

where ©r = hcBr/k is a characteristic temperature of rotation and depends on the rotational constant Br. Thus, we see that since hc/k = 1.439 cm K and Br is typically about 2 cm"1, then ©r is about 3 K, and hence for atmospheric temperatures ©r/T ^ 1 and hence the sum in the above equation can be replaced by an integral to give

while for polyatomic molecules of atmospheric interest, the rotational partition function varies as T3/2 (Herzberg 1945). The partition function for vibration of a diatomic molecule, neglecting anharmonicity effects, to a very good approximation for the lower levels (equally spaced vibrational levels), is

where ©v = hcuo/k is a characteristic temperature of vibration, typically about 3000 K. Since ©r ^ ©v we can write, ignoring the zero-point energy and the ©r value when v=0, ni = gjexp(-^©v/T) ^

n QvQr

We can sum over all the rotational lines, m, in the band to obtain the temperature dependence of the band strength. The value of the band strength k at some temperature T, compared to its value at some reference temperature Ts, is then given by k(T ) = K(Ts)RrRvRbRst, (4.89)

where the ratios R are associated with the rotational and vibrational partition functions, the Boltzmann distribution, and the correction for stimulated emission, are given by

Was this article helpful?

0 0
Guide to Alternative Fuels

Guide to Alternative Fuels

Your Alternative Fuel Solution for Saving Money, Reducing Oil Dependency, and Helping the Planet. Ethanol is an alternative to gasoline. The use of ethanol has been demonstrated to reduce greenhouse emissions slightly as compared to gasoline. Through this ebook, you are going to learn what you will need to know why choosing an alternative fuel may benefit you and your future.

Get My Free Ebook


Post a comment