SECTION H 



PHYSICAL BASIS OF THERMAL RADIA TION 



S. S. PENNER 



H,l. Introduction. The conventional and most successful approach 

 to engineering calculations of radiant heat exchange is described in the 

 following section. Included in the discussion are empirical rules and ex- 

 trapolation procedures. In order to appreciate the limitations involved in 

 the use of these empirical rules, it is essential to gain some understanding 

 of the physical principles which determine emitted and absorbed radiant 

 energies. Since a fundamental description of the phenomena involved is 

 particularly simple for the equilibrium radiation of gases, we shall con- 

 fine our attention to a brief survey of fundamental laws and to a quali- 

 tative outline of the methods used for calculations on the thermal radi- 

 ation characteristics of gases. 



H,2. Black Body Radiation Laws. A black body is defined as a body 

 which neither transmits nor reflects any radiation which it receives; a 

 black body absorbs all of the incident radiation. It can be shown that 

 the equilibrium energy of radiation emitted from the unit area of a black 

 body in unit time at a fixed temperature represents an upper limit for the 

 thermally emitted energy from unit area for any substance which is at 

 the same temperature as the black body. This definition of a black body 

 and the quantum mechanics principle of equipartition of energy [1, Chap. 

 2; S, pp. 546-550; 3, pp. 363-372] are sufficient to establish the Planck 

 black body distribution law, which expresses the equilibrium rate at which 

 radiant energy is emitted from a black body as a function of wavelength X 

 and temperature T. The Planck black body distribution law has been 

 abundantly confirmed by experiments. 



The spectral (or monochromatic) radiancy R^dX is defined as the 

 energy emitted, per unit time, from unit area of a black body in the 

 wavelength range between X and \ -\- d\ at the absolute temperature T 

 (in °K), into a solid angle of 2% steradians. The Planck black body dis- 

 tribution law is 



Ci d\ 



RldX = P^ _„_,T . (2-1) 



where Ci/tt and C2 are known as the first and second radiation constants, 



( 489 ) 



