12 FOFONOFF [chap. 1 



expansion coefficient is poorly defined by present measurements. Eckart (1958) 

 found the values 90 x 10-6 deg-i and 190 x 10-6 deg-i at OT and 1000 atm, 

 depending on whether a linear or quadratic expression is assumed for^o in (27). 

 A comparison of the coefficient of thermal expansion, (1/a) dajd^, computed 

 from (24) and (27) is given in Table I. The coefficients of compressibility, 

 — (1/a) da/Bp, and saline contraction, —(1/a) da/ds, as computed from the two 

 formulae, differ by about 1% or less. 



Table I 



A Comparison of the Coefficient of Thermal Expansion of Sea- Water at 35 %„ 



Salinity and Atmospheric Pressure as Computed from Equations of State, 



a/f (Knudsen, 1901) and as (Eckart, 1958) 



3. Entropy 



We can determine changes of entropy through the equation 



= '^dT-^dp-^ds. (28) 



if we know the specific heat, the thermal expansion and the thermal rate of 

 change of chemical jDotential. If these coefficients are known at atmospheric 

 pressure, their values at elevated pressures can be computed from (18) and (19) 

 using the equation of state. As indicated earlier, djjLJdT cannot be completely 

 specified in terms of equilibrium-state properties, and, hence, entropy is also 

 incompletely specified. 



Until recently, oceanographers have used specific heat values obtained by 

 Thoulet and Chevallier (1889) for a range of sea-water densities (salinities) at a 

 temperature of 17.5°C and at atmospheric pressure. In the absence of measure- 

 ments at other temperatures, the specific heat was assumed to decrease with 

 temperature in the same way as pure water. Cox and Smith (1959) carried out 

 a complete determination of the specific heat over the range - 2°C to 30°C in 

 temperature, 0%o to 40 %o salinity, at atmospheric pressure. The variation of 



