As previously mentioned, the thermal state of sea water is
determined by the specification of three independent thermal
properties. We will select as the fundamental thermal
variables the temperature T, the salinity S and the
pressure p. For each combination of these variables, the
density of the sea water is asserted therefore to be uniquely
specified. The relationship between the four variables 
can be written formally as
and is referred to as the equation of state. The actual form of function f is established empirically.
It is convenient to express the equation of state in differential form as follows
or
where 
is the reciprocal of 
( = specific
volume) and where
is the coefficient of thermal expansion at constant pressure and salinity,
is the coefficient of saline contraction at constant temperature and pressure, and
is the isothermal compressibility coefficient at
constant salinity.
The values of these coefficients depend upon the fundamental
variables T, S and p. Values of e are given in
Table 9 of The Oceans (p. 60) and values of the mean
compressibility are given in Table 15 (p. 68). For usual
conditions of temperature and salinity, the value of e
is positive but varies from nearly zero to
about 
per 
corresponding
to a range of temperature of about 
.
The value of e increases with an increase in temperature,
salinity, or pressure. The mean value of K is about
per decibar and varies only
slightly with temperature, salinity and pressure. However,
these slight variations are important in connection with the
transmission of sound in the sea. The mean value of
b is about 
per ppt salinity and
varies only slightly with temperature, salinity and pressure.
As a rule of thumb, an increase of of one part per
thousand can be brought about by:
(from 
to 
at 36 ppt salinity and atmospheric
pressure);