foote: total emissivity and resistivity 



Jk = C,\ 



-5 



e\T - 1 



-1 

 (3) 



where T is the absolute temperature and c^ = 1.4450 cm. deg. 

 The total energy (any arbitrary unit) radiated by a black body 

 is given by the integral of equation (3) : 



I 



Jxd\ (4) 



The total energy radiated by a nonblack metal may be ex- 

 pressed as the integral of ihe Planck relation multiplied by the 

 monochromatic emissivity : 



J'= r J^E^dX (5) 



Jo 



If the total emissivity E oi a, metal is defined as the ratio of 

 the energy emitted by the metal at an absolute temperature T 

 to that emitted by a black body at the same temperature, one 

 obtains the following relation: 



^ - T - /.V.rfx ^^> 



Equation (6) may be converted to the gamma function form 

 and is hence readily integrable. One thus obtains the following 

 expression for the total emissivity of a metal: 



E = 0.5736 VrT - 0.1769 rT (7) 



where T is the absolute temperature of the radiating metal and 

 r the volume resistivity in ohms cm at this temperature. 



It is therefore apparent that the total emissivity of most 

 pure metals should increase with increasing temperature both 

 because of the increasing value of T in equation (7) and because 

 of, in general, the increasing volume resistivity. The increase 

 in total emissivity with increasing temperature has been ob- 

 served in nearly all of the extremely few instances where this 

 quantity has been measured.^ 



^ Langmuir, Trans. Am. Elec. Chem. Soc, 23: 321. 1913; Randolph and Over- 

 holser, Phys. R., 2 (2) : 144. 1913; Burgess and Foote, Bureau of Standards 

 Scientific Paper 224. 



