Let 
be the specific Gibbs potential
or "free energy" of the fluid (J/kg), then
Also define the specific enthalpy (J/kg)
and the specific internal energy (J/kg)
From (2.1) it follows that
and from (2.4) and (2.6)
and from (2.5) and (2.6)
Let
then the specific volume is
the specific entropy is
and the chemical potential is
Auxiliary definitions give the adiabatic lapse rate (from 2.16) as
the sound speed (using 2.15 and 2.16) as
The potential temperature definition is
where 
is a standard pressure usually taken as one
atmosphere, or
where 
absolute potential temperature.
This is the temperature which a sample of fluid would have if
brought to reference pressure adiabatically and without
change of S.
Also, 
and 
are the values of 
and
for P, T, and S taken as , 
, S.