H • PHYSICAL BASIS OF THERMAL RADIATION 



respectively. The quantities Ci and C2 may be expressed in terms of the 

 fundamental physical constants c (velocity of light), h (Planck's const), 

 and k (Boltzmann const). Thus Ci = 2TC~h = 3.742 X lO"^ erg-cm^-sec"^ 

 and Co = hc/k ^ 1.439 cm-°K. For 



XT ^ 0.3 cm-°K, R^dX 



is given, with an accuracy of better than one per cent, by Wien's radi- 

 ation law 



For XT' ^ 77 cm-°K, the Rayleigh- Jeans radiation law 



iRl).,dx = (^) dx 



gives an accuracy of better than one per cent. 



For a given temperature the maximum value of R^ is found from 

 Eq. 2-1 to be 



(Ri)^^^ = 2I.2OC1 (Jj (2-2) 



and to occur at the wavelength X^ax determined by Wien's displacement 

 law 



^ra..T = -%- ^ 0.2898 cm-°K (2-3) 



The total radiant energy emitted from unit area in unit time by a 

 black body over all wavelengths into a solid angle of 2ir steradians is 



W 



= IJ RldX = aT^ (2-4) 



where a is known as the Stefan-Boltzmann constant and has the numeri- 

 cal value 0- ^ 5.670 X lO"'^ erg-cm-2-(°K)-4-sec-i. The quantity W is 

 variously referred to as the radiant flux per unit area, total emissive 

 power of a black body, or radiancy. The (normal) radiant intensity is 

 the radiant energy emitted in a direction perpendicular to the black 

 body, per unit solid angle, per unit area, per unit time; it is identified by 

 the symbol J and equals W/ir. 



The quantities R^ (ie^)„,„,, RU(Rl)n..., SUl-dX', TF,and (1/T7) JU^^X' 

 have been tabulated [4] for the wavelengths and/or temperatures which 

 are likely to be encountered in practice. 



The frequency v is related to the wavelength X through the expression 



V = ^ (2-5) 



< 490 ) 



