306 PHENOMENA, ATOMS, AND MOLECULES 



at a higher temperature To, the molecules leaving the surface have a 

 temperature T intermediate between T2 and Ti such that 



T-T^ = a{T.-T,), (2) 



where a is a number less than unity which has subsequently been called 

 "accommodation coefficient" by Knudsen. 



Smoluchowski considered that the same value of / or a could be applied 

 to the phenomena of both viscosity and heat conductivity and thus cal- 

 culated a relation between the coefficient of slip and the temperature drop 

 at the surface. 



Knudsen (/. c), on the other hand, considered a to be unity in the case 

 of viscosity, although not in the case of heat conduction. 



Baule ^"^ attempts to solve this difficulty by analyzing the probable 

 mechanism by which heat or momentum is transferred from gas to solid. 

 Baule assumes that the solid consists of a cubic space lattice of elastic 

 spherical molecules or atoms which are vibrating about their equilibrium 

 positions with a mean kinetic energy corresponding to the temperature of 

 the solid. 



The molecules of the gas strike against those of the solid and rebound 

 from them according to the laws of elastic collision. If Ex be the mean 

 kinetic energy of the incident molecules, Eo the mean energy of the mole- 

 cules of the solid, and £' the mean energy of the gas molecules after one 

 collision with the molecules of the solid, then 



;?= /:;■ r.:% - (4) 



£' = /?£, + (!-/?) £2, (3) 



where 



{m\ -\- mo)' 



Here iiti is the mass of the gas molecules and in-z is that of the molecules 

 of the solid. 



It is evident that many of the molecules make more than one collision 

 before leaving the solid surface. Baule assumes that, of all the molecules 

 striking the surface, the fraction v make only one collision, while the 

 fraction i — v are absorbed and thus make such a large number of collisions 

 that they reach complete equilibrium with the solid before leaving it again. 



Thus, if E is the mean energy of all the molecules leaving the surface 

 we have 



£ = v£'-f (i-v)£2, (5) 



whence from (3) 



£ = /?v£i4- (i -/5v)£o. (6) 



^^ Ami. Phys., 44, 145, 1914. 



