SECT. 1] PHYSICAL PROPERTIES OF SEA-WATER 15 



The ratio of specific heats is 



Cp 



y = — 

 Cv 



1 + 



-1 



Cp{8vl8p) J ^^*^ 



and is greater than unity because dv/Bp is negative. The ratio varies from 

 1.0004 at 0°C to 1.0207 at 30°C for a sahnity of 34.85%o (Matthews, 1923). 



Two concepts which find particular use in the analysis of deep-water struc- 

 ture in the ocean have been developed from the equation for entropy change 

 (28). These are the adiabatic lapse rate of temperature and potential tempera- 

 ture. The equation for the adiabatic lapse rate of temperature was first derived 

 by Sir William Thomson (1857). Potential temperature was first used in 

 oceanography by Helland-Hansen (1912). 



If a layer of sea-water is completely mixed so that two elements of water, 

 anywhere within the layer, are indistinguishable when brought together to the 

 same pressure, the layer must have constant salinity and entropy. This may 

 be seen from the fact that the comparison of the elements within the layer can 

 be made by a reversible and, hence, isentropic, process. If either salinity or 

 entropy are different, the mixing cannot be complete. Consequently, for a 

 completely mixed layer of sea-water, we may write (28) as 



dr] = {cplT)dT-{8vldT)dp = 

 or 



\8pJ^ Cp 



where F is called the adiabatic lapse rate of temperature or adiabatic tempera- 

 ture gradient. Values of F for various temperatures, pressures and salinities 

 can be found from the graphs shown in Fig. 4. Coefficients for an empirical 

 formula for F are given in Table III. Both the graphs and formula are based on 



Table III 



Formula" for the Adiabatic Lapse Rate of Temperature, F, in Terms of 

 Temperature (°C), Salinity (%o) and Pressure (db) 



„ . lO^T dv „ „ „ . 



« Fofonoff and Froese, 1958. The precision of the formula is about 0.1% of F for the 

 range 0° to 30X\ 20 to 40%o and to 10,000 db. 



