Page 50 - Basic physical chemistry for the atmospheric sciences

36 Basic physical chemistry

where e and T are the vapor pressure and temperature of the system,
e
respectively, and e s is the saturation vapor pressur . For a droplet of
radius R, Eq. (2.53) becomes

ilE = 47TR u - n�1TR kT In (;) (2.54)
3
2
In subsaturated air e < e.; therefore, ln(ele.) is negative and 6.E is
always positive and increases with increasing R (Fig. 2 . 3 ) . In other
wor s , the larger the embryonic droplet that forms in a subsaturated
d
vapor the greater the increase in the energy of the syste . Since a
m
s y stem approaches an equilibrium state by reducing its energy, the
formation of droplets is clearly not favored under subsaturated condi­
tions. Even so, due to random collisions of vapor molecules, very
small embryonic droplets continually form (and evaporate) in a subsat­
urated vapor, but they are neither numerous nor large enough to
become visible as a cloud of droplets.
When air is supersaturated, e e . and ln(ele.) s positive, so that .:lE
i
>
in Eq. (2.54) can be either positive or negative depending upon the
value of R. The variation of .:lE with R for this case is also shown in
Figure 2 . 3 , where it can be seen that ilE initially increases with in­
=
creasing R, reaches a maximum value when R r, and then decreases
with increasing R. Hence, in a supersaturated vapor, embryonic drop­
lets with R < r tend to evaporate, but droplets that manage to grow by

Figure 2.3. Increase t:,.E in the energy of a system due to the formation of a
droplet of radius R from water vapor with pressure e; e. is the saturation
vapor pressure with respect to a plane surface of the liquid at the temperature
of the system.