SECT. 1] 



PHYSICAL PROPERTIES OF SEA-WATER 



25 



and salinities of the two phases. The rate of entropy production per unit mass, a, 

 is found by differentiating (57) with respect to time and substituting rj for cp. 

 The rate can be expressed in the form 



ma = 



m\m2 

 m 





{h2-hi) + 



dh 



dh ds 



{S2-S1) 



dh 

 dt 



+ 



dhi 



^"^1 ,1. r. \ ^^V / X 



, ,/^2 i^i \ / dsi 



ds 

 di 



(61) 



If the two phases have an area A in contact with each other, we can interpret 

 {mil A) dhildt as the flux of enthalpy, Fh, and {mil A) dsildt as the flux of salt, 

 Fg, from phase 2 to phase 1. Similarly, if the two phases have a mean thickness 

 Az and a mean density p, chosen so that pAAz = m, we can interpret 



Xh = 



&2 —'d'l 



T^ Az' 



X,, = 



/^2 P-l 



T2 Tl 



Az 



as the gradients of potential or forces acting between the two phases to drive 

 the exchange processes. In terms of the forces and fluxes, the equation for the 

 rate of entropy production becomes 



per = XhFh+XsFs 



(62) 



A general assumption of the theory of irreversible processes is that a flux 

 may be produced by any of the forces. Thus, in the general case we have the 

 possibility that a flux of heat or salt can be produced by both a gradient of 

 temperature and of salinity. The simplest formulation of the relationship 

 between fluxes and forces is obtained by assuming that the flux is linearly 

 proportional to the forces and may be specified by 



Fh = LhhXh + LhsXs 



for the flux of enthalpy and 



Fs = LshXh + LssXs 



(63) 



(64) 



for the flux of salt. The coefficients may be functions of temperature, pressure 

 and salinity, but are not functions of the forces themselves. The coefficients 

 must also satisfy the requirement that the entropy production be always 

 positive. This requirement is met if the coefficients satisfy the inequality 



LhhLss > 



Lhs + L 



sh 



The flux of enthalpy can be written 

 Fh = Fq — 



= Fg + hsFs, 



8T \T 



^ 0. 



F.. 



(65) 



(66) 



