Now if we define the potential temperature according to:
then eq.(6) may be written as:
or
if one ignores the very small contribution made by the last term.
For adiabatic, reversible changes, the potential temperature as defined above is the temperature an air parcel would have if brought to the reference pressure (usually taken to be 1000 hPa.). Since the is conserved in dry adiabatic motion then so also
is the potential temperature.
The entropy of saturated water vapour ( ) at temperature is equal to the sum of the entropy of {\em liquid} water (at temperature ) and the entropy required to evaporate the water isothermally. If is the specific heat of liquid water and is the latent heat of vaporization then:
and if is reasonably assumed constant:
ignoring an arbitrary constant for the moment. Now if this saturated air parcel contains liquid water droplets at
the same temperature then there will be an additional entropy contribution :
on the assumption that this dominates any contribution from surface tension forces in the surface of the droplets.
Therefore, the entropy of a saturated air parcel containing of dry air, of water vapour and of liquid water condensate is: