102 Dr. R. D. Kleeman on the Kinetic 



bulb of the thermometer. Now there must exist a large 



number of points in a liquid, which like the molecules are 

 in motion, at which the forces of the surrounding molecules 

 neutralize one another. It follows from the above result 

 that the thermometer indicates a temperature corresponding 

 to the velocity a molecule has when passing through one 

 of these points. This velocity is equal to the velocity the 

 molecule has in the gaseous state at the same temperature. 



The effect of molecular attraction is to make the molecules 

 in a mass of matter approach one another on collision with a 

 greater velocity than they would have if they did not possess 

 this property. The average velocity of a molecule may thus 

 be much larger than the minimum velocity which corresponds 

 to its temperature. 



The Average Velocity of a Molecule. 



Van der Waals, in deducing his equation of state, assumes 

 that the velocity of the molecules in a substance is not 

 influenced by their attraction upon one another. But it 

 can be easily shown that this assumption cannot be even 

 approximately true. The effect the molecular attraction 

 has on the velocity and shape of path of a molecule cannot 

 be exactly calculated, owing to mathematical difficulties, 

 and a want of knowledge of the correct form of the law of 

 molecular attraction. But numbers can be obtained which 

 show that the average velocity in a liquid is several times 

 that corresponding to the temperature of the substance. 

 which is the minimum velocity. 



Suppose that the volume 1 of a gram of liquid at a low 

 temperature in contact with its saturated vapour changes 

 by dr. The energy spent in overcoming the attraction 



between the molecules is therefore ,\ where L denotes 



av 



the heat of evaporation of the liquid. The distance between 

 iwo molecules is changed by (■==- 1 during the pn 



where X denotes the number of molecules per c.e. of the 

 liquid : and the rate of expenditure of energy per unit 

 distance per molecule is therefore 



dh i ,/i. m 



since Nm a = p and r— . where n den • densitv and 



