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:

- a decrease of about (from to at 36 ppt salinity and atmospheric pressure);
- an increase of about 1.2 ppt salinity; and
- an increase of about 200 decibars pressure.

Mon Dec 1 08:50:29 CST 1997