4 FOFONOFF [chap. 1 



There is still a need to determine or re-examine many of the basic properties 

 of sea-water. For this reason, more effort is taken here to develop) the thermo- 

 dynamical basis for these properties in order that the relationships among 

 them may be brought out more clearly and systematically. The properties are 

 discussed, therefore, in three parts. Properties necessary to describe thermo- 

 dynamic equilibrium are considered first, then the additional properties 

 required to characterize the non-equilibrium state, and, lastly, other properties 

 that are of interest. 



Because of the raj)idly increasing use of electronic digital computers for 

 processing oceanographic data, empirical formulae in current use for some of 

 the more frequently computed properties are included. Unfortunately, recent 

 studies indicate that most of these formulae are of inadequate accuracy and, 

 therefore, cannot be recommended for general future usage. We are sorely in 

 need of a complete overhaul of existing tables and formulae for the routine 

 calculation of sea-water properties. However, it would not be advisable to 

 propose changes that are not supported by more complete and accurate 

 determinations of the properties than we have at present. 



1. The Equilibrium Thermodynamic State 



The continual exchange of energy and matter across the boundaries of the 

 ocean prevents the establishment of a complete thermodynamical equilibrium. 

 In general, the transport of water, heat and salt by currents greatly exceeds 

 that of molecular processes associated with the tendency for the ocean to 

 approach thermodynamical equilibrium. However, at sufficiently small scales 

 of motion, molecular processes become significant and even dominant. Hence, 

 it is necessary to formulate and examine the conditions under which equilibrium 

 is attained and to determine the physical properties required to describe the 

 equilibrium state. We shall examine the equilibrium state from the physical 

 point of view, treating the dissolved salts as a single component and ignoring 

 chemical reactions and equilibrium conditions that alter the ionic structure in 

 sea-water. 



Because of gravity, the pressure in the ocean increases continuously with 

 depth. This means that we cannot have a uniform phase of finite vertical 

 extent. We must consider the ocean as being made up of an infinite number of 

 phases in its vertical structure. Each of these phases forms an open system free 

 to exchange heat and matter with adjacent phases. It is, therefore, more con- 

 venient to formulate the thermodynamical relationships in terms of a system 

 of unit mass and to consider finite systems in the ocean in terms of integrals 

 with respect to mass over all of the phases within the system. 



The thermodynamical relationships for a sea-water system can be obtained 

 from a general statement of the first law of thermodynamics for a multi- 

 constituent system within a gravitational field (e.g., Guggenheim, 1950, p. 356). 

 Changes of the total energy, E, of a system of total mass, M, at a gravitational 

 potential (geopotential), 0, are given by 



