of the Liquid and Gaseous States of Matter. G85 



velocity of translation ; further, the velocity of each molecule 

 is continually changing, the distribution of velocities among 

 the molecules at any instant being given by Maxwell's law 

 or some law similar to it. A certain number of molecules 

 will therefore each second obtain sufficient kinetic energy to 

 be able to get away from the attraction of the molecules of 

 the liquid, equilibrium being produced when the number 

 shot out of the liquid is equal to the number returning from 

 the vapour. When the volume of the vapour is decreased by 

 compression its density must remain the same, for the 

 number of molecules shot from the surface of the liquid per 

 cm. 2 is unaltered by the process, and therefore the number 

 coming from the vapour must also remain unaltered, and a 

 portion of the vapour must therefore condense to keep the 

 density constant. 



Now, suppose a cylinder which has one end closed and in 

 which a piston works contains some saturated vapour of a 

 liquid, and suppose we endeavour by moving the piston to 

 pass the vapour through those changes usually not realized 

 in practice. From a consideration of the law of attraction 

 of one molecule on another and the average density of rigid 

 materials, it follows that the attraction of the material of the 

 cylinder on the vapour will be very nearly equal to that of 

 the liquid corresponding to the vapour. The surface of the 

 cylinder will therefore be covered with a thin layer of vapour 

 which will be nearly as dense as the liquid. A small 

 increase of pressure only will therefore in general be 

 required to increase the density of this thin film, so that it 

 is equal to that of the liquid. When that stage is reached, 

 condensation of the vapour upon this liquid film takes place, 

 and its pressure then decreases till it is equal to that of the 

 ordinary pressure of the vapour in contact with the liquid. 

 The pressure remains constant on the volume of the vapour 

 being further decreased, and the vapour thus does not pass 

 through the relations between pressure and volume indicated 

 by theory. It appears, therefore, that if it were possible to 

 construct the cylinder out of material which has no molecular 

 attraction, the vapour could be passed without difficulty 

 through all the isothermal changes indicated by theory. 



From the equations of state given in this paper we can 

 deduce some relations of interest and importance. Referring 

 to the figure, it follows from thermodynamics * that the 

 amount of external work done in passing along the isothermal 

 from b to d is equal to the work done in passing from b to d 



* Winckelmann, Handbuch der Physik, Wtinne, p. 654, second 

 edition. 



