309-311] Dependence of Viscosity on Temperature 



257 



value of <r in question. The force of repulsion between two molecules at 



dT 



distance <r is accordingly R -= , or more conveniently, since we are regarding 



do~ 



or as a function of T, 



I dor 



In this way the variation of cr with T can be made to give us some idea of 

 the variation and magnitude of the intermolecular forces. 



310. It is found that the variation of K with the temperature can be 

 represented with tolerable accuracy by a formula of the form 



/ T \ n 

 ?f*(sf$) (583), 



where T is the absolute temperature, measured on the Centigrade scale, and 

 n is an index which is different for different gases, its value always being 

 intermediate between ^ and 1. The constant /c is of course the value 

 of K at C. 



By equation (582), K varies as T^a~ 2 , and hence by comparison with 

 equation (583), cr varies as T~^ n ~^. By differentiation, dT/da- varies as 



T 2 



- , and this again varies as cr n-i . 



We may say, then, that on the average, the force between two molecules 

 at distance r apart is ^ , where 



+ 1. 



.(584). 



In a later section we shall deduce this same equation from a discussion of 

 physical dimensions. 



311. The following table gives various observed values for n, together 

 with the corresponding values for s calculated from equation (584). 



J. 



17 



