done during the Evaporation of a Liquid. 4.05 
If a is a fraction it can be shown that the substance can exist 
in two phases. Thus suppose that some of the substance is con- 
tained in the cylinder of figure 1 in contact with the piston, and 
let the piston be displaced in the same way as before. The surface 
of the substance will go on shedding molecules till the density of 
the vapour is such that the same number of molecules are received 
upon the surface per second as leave it. This number must be 
larger than an, since the attraction of the vapour helps the molecules 
to get away from the liquid surface. But it must be smaller than 
n, for if equal to n it follows in the same way as before that both 
phases must have the same density, and hence there would be 
only one phase. The condition that another phase could exist 
in contact with the substance is therefore that a should be less 
than unity. When this condition is satisfied the phases are 
realizable in practice. Thus let a denote the value of a for a 
quantity of the substance whose density is less than that just 
considered. Now the value of n increases with increase of density 
of the substance, while that of a decreases, since the attraction 
the kinetic energy of a molecule has to overcome increases with 
increase of density. If the two surfaces of the substances which 
are of different densities are placed in contact, the values of 
a, , and an are increased along the boundary, since the attraction 
of each substance helps the molecules of the other substance to 
get away from it. But the increase is greater in the case of the 
less dense substance than in the case of the other, on account of 
it being bounded by a substance of greater density than itself, and 
the opposite applies to the other substance. Thus it should be 
possible to find a density for the second substance which is less 
than that of the first, so that when the substances are placed in 
contact with one another the number of molecules passing from 
one into the other is the same, in which case they will be in equi- 
librium. Upon reflection it will be evident that the existence 
of a surface transition layer does not invalidate the foregoing 
conclusions. 
The foregoing considerations show that when a substance is in 
the critical state a=1. Nowa molecule could get away from the 
surface of a mass of substance and out of the influence of its mole- 
cules after displacement of the piston in the process described only 
when its kinetic energy is equal to the energy expended in over- 
coming the attraction of the substance. The kinetic energy of a 
molecule in the substance that could be expended in this way is 
that which it has when passing through a point at which the forces 
of the surrounding molecules neutralize one another. For we have 
seen that when a substance is converted at constant temperature 
into the perfectly gaseous state this kinetic energy remains con- 
stant, the heat being expended in overcoming external and internal 
