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
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: