The total power absorbed by the CO2 molecules, PT, is found by summing overall vibrational-rotational transitions, i.e., where avdv is the integral absorption [25] of one J line over the CO2 absorption band, J is the rotational quantum number, av is the absorption coefficient of a line, Z7 is the sum over optically allowed transitions, and Bv is the specific intensity of the blackbody radiation, assumed constant and evaluated at 4.3 /zm. Implicit in the use of equation (2) is the assumption of an optically thin absorbing medium [23]. From equation (2) and the Planck function, Tp is found to be approximately Qvt43, where Q, is the vibrational partition function of CO2 [23]. After some mathematical manipulations [15], a final form of this equation can be obtained [26, 27]. Thus, the variation of PT as a function of Pv3 can be found [15]; Tvl and Pv3 can be determined iteratively from equation (1), and then the final form of equation (2) for the steady-state case, after the physical conditions have been specified. For the Doppler-broadened case, the small signal gain coefficient at a line center in the 10.6 /zm band of CO2 for a rotational quantum number J may be calculated using the approximately equation [22]: where gj is the rotational degeneracy factor, 0r is the characteristic temperature for rotation (0r^O.565 K for CO2) [23], m3 and nt are the number densities of the (001)
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