32 ECKART [chap. 2 



2. Thermodynamics 



Sea-water will here be treated as a two-component solution, consisting of a 

 solvent (water) and a single solute (salinity). The basic thermodynamic function, 

 which specifies many of the properties of such a solution, is its internal energy 

 (e erg/g) expressed as a function of its specific volume {v cm^/g), entropy 

 {rj erg/g deg) and salinity (*S' g/g) : 



€{V, -q). 



Its pressure, p, absolute temperature, 6, and chemical potential, /x, are then 

 calculable from the equations 



p = -deldv, e = deldri, /x = dejdS. (1) 



Other thermodynamic properties are defined in terms of the second deriva- 

 tives of e ; with a view to later application, they will be written in terms of the 

 small increments oi p . . . S: 



8p = -X8v+Y87^ + K8S 



86 = -YSv + Z8r] + L8S (2) 



S/x = -K8v + L8r] + M 8S 



where X, — Y, Z, —K, L and M are the second derivatives of e with respect 

 to V, 7) and S. These derivatives can often be related to more commonplace 

 thermodynamic coefficients. Thus 



X = p^c^ 



Y = p{y-l)la (3) 



z = eiCrs 



where p= l/v = density, a = coefficient of thermal expansion, c = velocity of 

 sound, and Cvs, Cps = specific heats at constant salinity and constant volume or 

 pressure, while 



y = CpslCrs = 1+a^cWICps. (4) 



Similarly commonplace expressions for K, L and M have not yet arisen in the 

 literature. The definitions 



Hpr = KdjY (5) 



Hev = LdlZ (6) 



H,r = MOIL (7) 



give the three //'s the dimensions erg/g. For reasons that will become clear in 

 Section 5 of this chapter, they will be called heats of diffusion, Hpv being the 

 heat of diffusion at constant pressure and volume, etc. 



Methods for the measurement of the heats of diffusion or, alternatively, for 

 their calculation from the measurement of related quantities have not yet been 

 devised. Of the three, Hpv is the most urgently needed quantity since it enters 

 into the final equations of motion (cf. equations (37), (43), and (47)). 



The third and higher derivatives of e may also be of importance, but will not 

 be investigated here. 



