H,3 • NONBLACK RADIATORS 



where c is the velocity of Hght (c = 2.998 X 10^" cm-sec~^) ; the wave 

 number co is the reciprocal of the wavelength, i.e. 



CO = i (2-6) 



From Eq. 2-1 and 2-5 it follows that the spectral radiancy in the fre- 

 quency range between v and v -\- dv 2ii the temperature T is given by 

 the expression 



^M^ = -^ ^n.nT _ 1 (2-7) 



Similarly Rldw is determined according to the equation 



Rldo. = 2-.^^ ^,J^_ ^ (2-8) 



H,3. Nonblack Radiators. The (hemispherical) spectral emissivity 

 ex of a substance is defined as the ratio of the spectral radiancy for the 

 given substance to the spectral radiancy of a black body. Thus the energy 

 emitted from a nonblack substance, per unit area, per unit time, into a 

 solid angle of 27r steradians in the wavelength range between X and X + dX 

 at the temperature T is 



i^x^X = exRldk 



if the spectral emissivity of the substance is ex. The nonblack substance 

 at temperature T is said to have (total hemispherical) emissivity e if the 

 total emitted energy, per unit area, per unit time, into an angle of 2ir 

 steradians is 



W' = eW = eaT^ 



The definitions of the spectral and total emissivities apply to dis- 

 tributed sources of radiation as well as to surfaces. A discussion of the 

 thermal radiation characteristics of gases (Art. 5) involves essentially 

 the development of basic procedures for the calculation of ex and e for 

 equilibrium systems of pure gases and gaseous mixtures. 



A simple example for the use of theoretical spectral emissivity rela- 

 tions is provided by Drude's law [5, Chap. 1] for pure metals, which 

 holds within a few per cent for wavelengths longer than about 2/x.^ Drude's 

 law relates the spectral emissivity to the electrical resistivity r (in cm) 

 and the wavelength X (in cm), viz. 



i 



ex ^ 0.365 ^- (3-1) 



^ The following wavelength units are often used in discussions of radiant heat 

 transfer: Angstrom unit A (1 A = 10~* cm) and micron /x (l/j. = 10~^ cm). The wave 

 number (reciprocal of the wavelength) is customarily expressed in cm~^ The frequency 

 is given in sec~^ 



< 491 ) 



