22 FOFONOFF [chap. 1 



colligative properties of sea- water, particularly vapour-pressure lowering, 

 would be desirable to improve our knowledge of the chemical potential difference 

 of sea-water. 



5. The Non-equilibrium State 



If two adjacent phases of a thermodynamical system are not in equilibrium, 

 they will tend towards an equilibrium by the exchange of heat and matter. 

 Thus, the thermodynamics of non-equilibrium states deals primarily with the 

 transport processes between adjacent phases. In the ocean, the transport pro- 

 cesses include conduction of heat, diffusion of dissolved salts and gases, and 

 rates of exchange of water with the vapour and solid phases. The related trans- 

 port process of momentum diffusion due to viscosity of sea-water can also be 

 included. 



The properties discussed in the previous section enable us to describe equili- 

 bria between adjacent phases of a sea- water system. In addition, we can use 

 these properties, together with the conservation laws of mass and energy, to 

 determine the equilibrium state towards which adjacent phases, initially not 

 in equilibrium, will proceed by the exchange of heat and matter. The final 

 state can be found by applying the second law of thermodynamics, which 

 requires the entropy of the final equilibrium state to be at a maximum. Thus, 

 by examining the entropy of possible final states having the same total energy 

 and mass, we can determine the distribution of temperature and salinity of 

 the equilibrium. However, we cannot determine the rate at which the system 

 approaches equilibrium. Therefore, the additional properties necessary to 

 characterize non-equilibrium states are the rates of the transport processes. 



It is evident that entropy is produced by the system in reaching equilibrium. 

 Hence, the concept of entropy production and particularly the rate of entropy 

 production forms the central core of non-equilibrium theory. The theory of 

 non-equilibrium states (more often referred to as the thermodynamics of 

 irreversible processes) can be applied to heat conduction and salt diffusion in 

 the ocean to develop the general equations describing these phenomena. The 

 treatment is simplified by assuming the dissolved salts to behave as a single 

 solute. 1 



The basic concepts of the non-equilibrium theory are introduced by con- 

 sidering an elementary sea-water system consisting of two homogeneous 

 elements of sea-water in contact with each other along a portion of their 

 boundary. We assume that these two adjacent phases are at a constant pressure 

 jp and are initially characterized by temperatures d'l and ^2, salinities S\ and Sz, 

 and masses mi and mz. We assume that the system is closed so that no salt or 

 water is exchanged across the outer boundary and, also, that no heat is added 



1 This assumption is an over-simplification. Some fractionization of sea-water con- 

 stituents will occur because of differing diffusion rates for various ions. However, because 

 of the lack of experimental studies of diffusion in sea-water and the fact that the treatment 

 presented here can be readily extended to a system of several diffusing components, only 

 the single-component system is discussed. 



