1. Surface Effects in Condensation
If we compress a gas isothermally condensation
is suppose to start at point O, and if we compress
further the pressure is suppose to remain constant..
Actually the pressure will often follow the dotted line.
Along this line the system is not in equilibrium, however,
the slightest jar will abruptly reduce the pressure to
the correct value.
supersaturation
supercooling P O’ O v
Similarly, if a liquid is expanded beyond the point O’ it will sometimes follow the
dotted curve, but this would not be in equilibrium. These phenomena are
respectively known as supersaturation and supercooling.

2. Surface Effects in Condensation
Vapor pressure as we have discussed this in class is the pressure at which a gas
can co-exist in equilibrium with an infinitely large body of its own fluid. we denote
this by the quantity,
The pressure at which the gas can co-exist in equilibrium with a finite droplet,
of radius r is not but a higher pressure,
The difference between these pressures is due to the surface tension of the
droplet.
Suppose a droplet of liquid is placed in an external medium that exerts a pressure
P on the droplet. Then the work done by the drop on expanding is
and

3. Surface Effects in Condensation
Integrating for a spherical drop of radius r,
is the internal energy per unit volume of an infinite drop.
The Gibbs potential for this can be written in the form
For the droplet in equilibrium with its vapor at fixed pressure and temperature
the Gibbs potential must be a minimum. This condition determines a relation
between P and r for a given T.

4. Surface Effects in Condensation
Let the mass of the droplet be ml and that of the vapor mv. Then the
total Gibbs free energy of the system can be written as
Suppose the drop undergoes an infinitesimal change in its radius owing to
evaporation such that,
Equilibrium is determined by the condition:
Since:
is the density of the liquid.

5. Surface Effects in Condensation
Equilibrium is determined by the condition:
This condition can only be met if the quantity
in the bracket is zero
Since
Equilibrium is defined by
Consider now a variation of this equilibrium with pressure.
Recall:

6. Surface Effects in Condensation
Since the density of the liquid is much larger than that of the gas,
Also assume that the vapor is sufficiently dilute so that it behaves as an ideal gas,
where m is the mass of a gas atom.

7. Surface Effects in Condensation
Rearranging and solving for
Integrating both sides of this equation, we find P as a function of r at fixed
temperature.

8. Surface Effects in Condensation
Recognizing that
is the atomic volume of the liquid, we can rewrite this
This is known as the
Kelvin Equation.
constant T

9. Surface Effects in Condensation
It is only “recently” that the Kelvin equation has been validated
fluid/vapor equilibrium. T’ T’
Thermal shield
cyclohexane T