SECT. 1] PHYSICAL PBOPERTIES OF SEA-WATER 7 



The Gibbs-Duhem equation (9) can. also be expressed in the form 



dfx^ = -L + s^jdT+lv-s^\dp-s^ds, (10) 



which is equivalent to 



= —rjvfdT + Vyidp — s-^f-ds. 



8s 



By analogy with a pure-water phase, we can interpret rjv/ as the partial specific 

 entropy and Vw as the partial specific volume of water in the sea-water phase. 

 We can define other thermodynamic potentials in the usual way, i.e. 



h = €+pv specific enthalpy 



/ = e—Trj specific free energy 



g = e — T7)+pv specific thermodynamic potential (Gibbs 

 function). 



Temperature, pressure and salinity are measured directly in the ocean. 

 These variables can then be used to calculate other properties, including the 

 depth of the observation; i.e. its location relative to the geopotential field. 

 Therefore, these variables are considered to be the independent variables in the 

 subsequent development. 



The appropriate function to describe the thermodynamical properties of a 

 phase in terms of temperature, pressure and salinity is the Gibbs function g. 

 From the first derivatives with respect to the independent variables, we obtain 



81 



eg 



dp 



-k = -" ('^) 



■,p = " <•=" 



a. = " <'*) 



and from the second derivatives 



d~g dr) Cp 



where Cp is the specific heat at constant pressure, and 



8^g dfx dtj 



dT 8s ^ JT ^ ~8s 



8^g 8v 8r) 



8T 8p ^ ~8T^ "Jp 



8^g 8v 8fjL 



8s 8p 8s 8p 



(15) 



(16) 

 (17) 

 (18) 



