Chemistry and Physics. 481 



Then, the energy absorbed per second by the body is expressed 



by 



s/a. 



.EdX 



The energy radiated per second is given by 



RdX 



sfa 







For thermal equilibrium these two quantities must be equal^ 

 hence 



CO 00 



This equation contains but one unknown quantity — the equili- 

 brium temperature T — and it always gives one, and only one^ 

 value for T. The numerical solution is always easy when the 

 different functions that enter in the equation are given by 

 tabulated data. The radiation equation F has a known analyti- 

 cal form. 



The special cases outlined below depend upon a simplification 

 of the general equation. The hypothesis is introduced that the 

 incident radiation comes from a hlach body at a given tempera- 

 ture © and subtending a small solid angle O at the receiving 

 body. The problem is accordingly reduced to that of the 

 thermal equilibrium between two bodies isolated in space, of 

 which one, the emitting body, has a black surface maintained at 

 a given temperature, while the other, the receiving body, has 

 arbitrary absorbing properties and acquires a temperature which 

 is to be determined. 



(1) Black or Gray Body. — Then 4>{X) is a constant that dis- 

 appears from the equation. The integral of F is proportional 

 to T^ so that 



T=®3l'' (1) 



where M == tttj/Q. This result can also be derived at once from 

 the law of Stefan. 



(2) Receiving Body having One Absorption Band. — The wave- 

 length of the center of the band is symbolized by Aj. The width 

 of the band must be small as compared with Aj, otherwise it is 

 arbitrary. The law of absorption within the band no longer 

 enters into the analysis, and it is not at all necessary for the 

 absorption to be complete for any wave-length. Using Planck's 

 radiation formula for F{X,T) Fabry shows that 



