H • PHYSICAL BASIS OF THERMAL RADIATION 



Since the electrical resistivity is roughly proportional to the first power 

 of the temperature for many metals, it follows that the total emissive 

 power of many metals varies as T within the range of validity of Eq. 3-1. 



H,4. Basic Laws for Distributed Radiators. For thermodynamic 

 equilibrium one can deduce Kirchhoff's law, which states that the 

 spectral radiancy of any substance equals the product of the spectral 

 absorptivity P'^ and the spectral radiancy of a black body.^ In other 

 words, the spectral emissivity €„ and the spectral absorptivity P'^ are 

 identically equal. It is convenient in practice to introduce the product of 

 two-dimensional parameters for the dimensionless spectral absorptivity 

 P'^. Following customary procedure we write for distributed radiators 



P: = P^dX (4-1) 



where P„ is termed the spectral absorption coefficient and is expressed in 

 cm""^-atm~^ or in ft~^-atm~\ with the pressure referring to the actual 



^ dX = pdX [^ 



■X = lp- 



Fig. H,4. Schematic diagram for the determination of the basic spectral emission law 

 for distributed isothermal radiators. (X represents optical density, p equals the partial 

 pressure of the radiator, and I and dx are geometric lengths.) 



pressure of radiators responsible for absorption at the wave number w; 

 correspondingly, the optical density dX, which represents the product of 

 a geometric length and the partial pressure of the radiators, must have 

 the dimensions of cm-atm or ft-atm, respectively. 



Consider now a system of isothermal radiators at pressure p dis- 

 tributed uniformly through a region of geometric length I. The optical 

 density of a region of infinitesimal geometric length dx is dX = pdx] the 

 optical density of the region of geometric length lis X = pi. A schematic 

 diagram is shown in Fig. H,4 in which the abscissa has the dimensions of 

 optical density. It is desired to obtain an expression for the total spectral 

 radiancy from the isothermal distributed radiators located in a column 

 of geometric length I. Let the spectral radiancy incident on the face A be 

 jRo.- The change in spectral radiancy corresponding to the region of optical 



^ The choice of the wave number w for identification of the spectral region is, of 

 course, arbitrary. Either the wavelength X or the frequency v may be used if desired. 

 The statement that P^ is independent of the intensity of the incident radiation may 

 be regarded as an experimentally established fact. This result follows also from 

 molecular considerations concerning the relation between transition probabilities and 

 absorption coefficients. 



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