THERMODYNAMICS OF RADIATION. 335 



ON as axis. A ring between 6 and 8 + dO will have area ZTrrsind.rdO, 

 and the radiation passing through it will be 



ydSco8g.2irrBiiig.nZg = 27 rNdSsin0cosfcZ0 



r 2 



The total radiation RcZS is obtained by integrating this over the 

 hemisphere, i.e. from 6 = to 6 = ^, and we get 



whence R = fl-N 



3. The Energy Density in a fully Radiating Enclosure. The energy 

 density E can be expressed in terms of R or N. For let the whole 

 sphere (Fig. 190) be sending out radiation ; that passing through O comes 

 normally from every element of the surface. If U is the velocity of 

 travel of the radiation, the energy density at O, due to an element c/S, 



. , NrfS . NrfS , , , , .. 



will be --JJ since ^- passes per second through a sq. cm. at O, and it 



travels U cm. in the second. Then the energy per c.c. is - or 



u u 

 The Pressure on a Fully Radiating Surface. Put at 



(F.g. 190), a sq. cm. of fully radiating, fully absorbing surface at the 

 temperature o f the enclosure. The energy density of a pencil falling on 



it from an element dS> of the sphere is - , and if cS is at the end of 



UH 



a radius making 6 with ON this produces pressure - 



Ur 2 



If we divide the hemisphere into rings each of area 2irr z sin0d0, then 



..2 



total pressure due to incident radiation = / 27ZT 2 Ncos 2 #sin#e?0 



7. 



27TN 



3U 



But the radiation issning from the area at will be equal in every 

 direction to that incident, so that this will be doubled, and we shall have 



-w-ro-i 



Relation between E and 6 in full Radiation. The Fourth 



Power Law. Let us imagine a sphere of which the inside surface 

 can be made, at will, fully radiating or totally reflecting. Let us suppose 



