SECT. 1] PHYSICAI. PROPERTIES OF SEA-WATER 23 



to the system. Under these conditions, it can be shown that maximum total 

 entropy is attained when the temperature and sahnity of the system become 

 uniform. We characterize the final phase by the temperature d-, salinity s, and 

 total mass m. 



As the two initial phases proceed towards equilibrium, both total mass and 

 energy must be conserved. We can assume that there is no net exchange of 

 mass between the two phases during diffusion in order to avoid convective 

 terms in the conservation equations. ^ 



The conservation of total mass and of salt is expressed by 



Am = m — {mi + m2) = (53) 



and 



Ams = ms — {miSi + m2S2) = 0. (54) 



Therefore, the change of salinity in each phase on reaching equilibrium is 



Asi = s — si = {m2lm){s2-si) 

 As2 = S — S2 = —{'milm){s2 — si). 



As no heat, salt or water is exchanged across the outer boundary, the total 

 internal energy me is changed only by the work done on the system by the 

 pressure acting on the outer boundary. Thus, the change of internal energy is 



Am€ = me— {mi€i + 'm2€2) = —pAmv 



= —p[mv — {miVi + m2V2)], 



where Amv is the total change of volume of the system. Rearranging terms, 

 remembering that pressure is assumed to be constant, we obtain 



A'm{€+pv) = Amh = 0, (55) 



which indicates that the total enthalpy of the system remains constant. 

 Changes of enthalpy in each phase on reaching equilibrium are 



Ahi — h — hi = {7n2J'm){h2 — lii) 

 Ah2 = h — h2 — — {milm){h2 — hi). 



We can compute the change of any other property, cp, from the general 

 equation 



Anup = m A(p = m(p — {'mi(pi + m2(p2), (56) 



provided we know 99 as a function of salinity, pressure and enthalpy. If the 

 initial phases differ only slightly from each other, we can express (56) in terms 

 of the initial differences of enthalpy and salinity by expanding cpi and 992 in 



1 A more general development of the theory, including convective terms, is given by 

 De Groot (1952). The results are the same for the particular system considered here. 



