340 HEAT. 



Now let us apply this to radiation originally of wave-length A in a 

 perfectly reflecting sphere, which is expanding with velocity 



= dr 

 U ~~dt 



If a ray strikes the surface at to the normal, its path between succes- 

 sive reflections is 2rcos#, and it strikes the surface ^ times per 



second. At each reflection its wave-length is increased by 



dA = A. 



U 



so that the increase per second is 



dA ZucosO U 



-77=A . ===^- X 



dt U 2rcos0 



r 



Xdr 

 or = - -=- 



r dt 



Then integrating, - is constant as the sphere expands, or the wave- 

 length is proportional to the radius. 



Change of Energy in Radiation of a given Wave-Length in an 



Adiabatic Expansion. Let us suppose that a spherical enclosure only 

 contains one kind of radiation of wave-length X, of energy density e, and 



exerting pressure p = If the radius increases from r to r + dr in an 



adiabatic expansion, the original energy is equal to the new energy + the 

 work done ; then 



4 4 e 



e . TjTrr 8 = (e + de) . -=ir(r + dr) 3 + ^ . 4*ndr 



de .dr a 

 whence \- = u 



e r 



and integrating er 4 constant. 



Change of Energy of each Wave-Length in Adiabatic Ex- 

 pansion of full Radiation. We shall assume that the above result 

 applies to each wave-length separately when we have full radiation. 

 If a sphere, then, containing full radiation expands from radius r to 

 radius r', 6 changing to & where rO = r'& (p. 338), then 



or A.0 is constant during the change. 



