14 FOFONOFF [chap. 1 



formula for the specific heat of pure water can be constructed in two parts, 

 using the measurements of Osborne et al. (1937). For temperatures above 

 33.67°C 



c/(,^) = 4.1784+8.46x10-6(^-33.67)2 (31) 



and below 33.67°C 



CpQ{d') = 4.1784+(8.46 + 26.19e-o-048*)x 10-6(,?-33.67)2, (32) 



where e is the natural logarithm base. These two formulae reproduce tabulated 

 values of CpO to within 2 parts in 10^ over the range 0°C to 100°C. The use of 

 the two-part formula gives a discontinuity in B^Cp^jdd'^ at 33.67°C of approxi- 

 mately 1% of the magnitude of the second derivative. The primary reason for 

 using the two-part formula is that &' is greater than 33.67°C for salinities in 

 excess of 30 %o for all temperatures above freezing. Thus, for most oceano- 

 graphic work, only (31) is required. 



The specific heat of sea-water at elevated pressures has not been measured, 

 but is calculated from (19). Coefficients for an empirical formula, based on (24) 

 and (25), for the effect of pressure on specific heat are given in Table II. The 

 specific heat at constant volume, Cy, of sea- water has not been measured, but can 

 be computed by using the auxiliary equation 



8v ,^ dv , 



(33) 



Table II 



Formula" for the Change of Specific Heat of Sea-Water, Cp, in Absolute Joules 

 per gram per degree Celsius, with Pressure as a Function of Temperature °C, 



Salinity %o, and Pressure db 



Cp{0)-Cp{p) 



T 



= f„w''p = ^^^"^p''"^' 



Aioo = +1.8185x10-'? ^120= +1.1649x10-11 



^101 = -5.574x10-9 A200 = -7.3867x10-13 



^102= +1.7417x10-10 ^201= +1.3574x10-13 



^103= -2.599x10-12 ^210= +4.824x10-14 



^110= -1.8117x10-9 ^300= +1.991x10-15 



Am = +1.5158x10-11 ^310= -2.5446x10-17 



« This formula has been constructed for electronic computer applications by the Pacific 

 Oceanographic Group (Fofonoff and Froese, 1958). Its precision is 0.2% of Cp for the range 

 -2° to 30°C, 20 to 40%o, and to 10,000 db. 



