36 LIBERATION OF ENERGY 



guided and tested by experiment, are accepted. The following 

 theory was first propounded by van't Hoff in 1885, and it has 

 been improved by later physicists. It allows the Second Law of 

 Energetics to be applied with conspicuous ease and clearness 

 to the theoretical investigation of the quantitative relations 

 between the properties of solutions. Matter is regarded as an 

 aggregation of particles (molecules), each of which is perfectly 

 elastic and structurally independent. Between them there exist 

 spaces. 



Two opposite forces are at work on molecules. 



(1) A Cohesive Force. Newton's Law^ states that every portion 



of matter attracts every other portion of matter. The stress 



between them depends on the mass of the particles and the distance 



m^ X 7^2 

 between them. Stress = 7- — , where m, and m^ are the masses 



of the particles and d the distance between them. 



(2) A Repellent Force (Real Kinetic Energy = \mv^). Every 

 molecule is free to vibrate in a straight line within the limits of 

 the intermolecular spaces. In a solid these spaces are small, 

 and therefore attractive forces are predominant. If a greater 

 kinetic energy be given to the molecules by means of heat, for 

 instance, their mean free path wdll be increased at a rate corre- 

 sponding to the coefficient of expansion. In a liquid the free path 

 of the molecules becomes sufficiently long to reduce the tractative 

 forces between the molecules to a value which is exactly balanced 

 by the forces keeping them apart. Pellation and tractation are 

 thus stalemate, leaving other forces, e.g. gravity, to determine the 

 arrangement of the molecules in space. 



If the temperature of the liquid be raised, some of the mole- 

 cules will acquire sufficient velocity to burst through the surface 

 layer and become free gas molecules. If these gas molecules 

 move away unhindered, other molecules from the liquid will 

 take their place, and the liquid will evaporate. If, however, 

 the liquid is kept in a closed space, the gas molecules which 

 leave its surface will be able to proceed no farther than the walls 

 of this space, and rebounding from these must eventually return 

 in the direction of the liquid. Some will strike the surface of 

 the liquid and will be retained by it. But the molecules still 

 continue as before to leave the surface of the liquid, so that, at 

 one and the same time, there are molecules entering and leaving 

 the liquid. When the pressure of the molecules leaving the 

 surface of a liquid balances the gaseous pressure above it, a 

 stationary state w^ill be reached, i.e. the same number of molecules 

 will be freed from the liquid as are being absorbed by it. That 



