deposited and then assuming it is carried to the walls by gaseous conduction. The amount of absorbed energy that goes into heating is obtained from Fig. 2 by considering the branching ratios. The fraction of the absorbed quanta (of average energy c) that ends up in producing CO2 (001) is Fkxa/[(ks + k2)a + X3], and hence the fraction contributing to heating (F') is The coefficient of heat conduction of a single gas is given by k = KcnCJl, where X is the mean free path, c the particle velocity, n the gas density, and C„ the specific heat of the gas at constant volume. The conduction is independent of the pressure (kn = constant) and cc The conduction mechanism is a transport of the hot particles with a diffusion coefficient Xc/3; hence, for a mixture of gases 1, 2, 3, where 1 = He, 2 = CO2, 3 = Br2, the resultant coefficient k is where mn = molecular weight, Cv,n = specific heat at constant volume, a„ = collision cross section, and 5 is defined as shown. The coefficient is in terms of K] as He has the highest conductivity and is regarded as the cooling gas. Assuming a one-dimensional heat flow out from the center of the gas to the enclosing side wall: dQ/dt = KAt (T - Tw/)l, where A, = unit cross section, / = distance, then a rough estimate of T at the center is obtained: The numerical constant assumes k, = 3.27 x 10-4 cal s'1 cm-1 K 1 (9). Apart from the one-dimensional approximation, Eq. 9 may also not be accurate if the radiation produces considerable dissociation. However, it can be seen that T is a function of (xpl/Ai), or a similarity law is obeyed (note that Tw contains C). Increasing p is equivalent to increasing either x or //A,. The gas ratios are described by (F'/S). Computer plots of Tat pressures of 1 and 3.6 Torr on an a-b plane are shown in Fig. 3 for C = 100. F = 0.5, Tw = 300 K. A flat laser is assumed of depth d = 2 cm, so / — d/2 and A/1 = 1 for unit area. Then Fig. 3a corresponds to p(Br2) = 0.17 Torr, and Fig. 3b corresponds to 3.7 Torr. The small increase in pressure causes a dramatic increase in Tbecause more radiation is trapped, yet the conduction does not increase
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