EVAPORATION AND CONDENSATION 307 



Since the mean energy of molecules is proportional to their temperature 

 Equation 6 may be written 



or 



r = ^vri + (i-/5v)r2, (7) 



(T-T^) = (l-M 0\-T,). (8) 



By comparing this equation with (2) it is seen that they are of the same 

 form and that (i — /5v) has the same significance as Knudsen's accom- 

 modation coefficient. 



In a similar manner Baule calculates the coefficient of slip. Let V\ be 

 the average velocity component, parallel to the surface, of the incident 

 molecules ; V2 the tangential velocity of the surface in the same direction, 

 and v' be the average velocity (parallel to the surface) of the gas molecules 

 which rebound from the surface after one collision. Baule shows that 



2/= Yt'i+ (i - y)^'2, (9) 



where 



(10) 



Of all the molecules striking the surface, the fraction v make only one 

 collision and are thus reflected with the velocity component given by (9), 

 whereas the fraction (i— v) are absorbed and thus finally leave the 

 surface with the average velocity component V2. If v be the average velocity 

 component parallel to the surface of all the molecules leaving it, then 



V = \i/ -\- {i — v)v'i, (11) 



whence from (9) 



V = yvt'i -|- ( I — yv)v2 ( 12) 



or 



(^,-7;i) = (l _ yv) (z/o-t^i). (13) 



The accommodation coefficient for viscosity is thus (i — Y^) instead 

 of the (i — /3v) which applies to heat conductivity. Thus Baule shows that 

 there is no theoretical justification for Smoluchowski's assumption that the 

 coefficients for heat conduction and viscosity are the same. 



In the case of hydrogen in contact with a platinum surface we have 

 mi = 2 and ;;/2 = 195, whence by (4) and (10), /? = 0.98 and y = .01. 

 If we take Knudsen's value a = 0.26 for the accommodation coefficient 

 (heat conduction), we find 1 — jjv = 0.26, whence v = 0.76. From this 

 we obtain (i — yv) =0.992, which should be the accommodation co- 

 efficient for viscosity. This is in good agreement v/ith Knudsen's experi- 

 ments from wliich he concludes that the directions of the reflected mole- 



