MOLECULAR MAGNITUDES 279 



velocities. The greater the number of such collisions 

 the greater will be the tendency of the molecules of 

 all the layers to come to a common speed and hence 

 the greater must be the force l which maintains the de- 

 sired difference. Other things being equal we should 

 expect that the greater the density, the greater will 

 be the viscosity. If th? molecules of a fast-moving 

 layer may travel, before collision, only to a near-by 

 layer, the molecules of which are moving with a speed 

 but slightly different, then the effect of the collisions 

 is not so great as it would be if the molecules move 

 past several layers and collide with those of a much 

 slower mass motion. Similarly we expect the effect of 

 the slow moving molecules to be less if they do not 

 move into far distant and rapidly moving layers and 

 hence that the greater the mean free path of the mole- 

 cules the greater will be the viscosity. These hypothet- 

 ical effects are not independent, for greater density 

 means smaller mean free path. The effect will also 

 depend upon the average molecular velocity. It may 

 be shown by reasoning similar to that followed hi 

 Chapter XIII, that 



c = vLd/3 (6) 



where d is density, v is average velocity, L is the mean 

 free path, and c is the coefficient of viscosity. For 

 example at 0C. for hydrogen c = 0.0000889, v = 169,200, 

 d = 0.0000898, and hence L = 1.76X10~ 5 cm. 



1 It is evident that energy is expended in maintaining this dif- 

 ference in mass velocity between two layers. The external energy 

 imparted to the molecules in a mass motion is thus seen to be con- 

 stantly degrading into molecular kinetic energy of haphazard mo- 

 tion. The average molecular velocity, and hence the temperature, 

 of the gas therefore increase. 



