The relative specific free enthalpy G(S, t, p) is determined quantitatively for seawater with salinity 0-40, temperature 0-40-degrees-C and pressure 0-1000 bar in the form of a polynomial. The new formula is consistent with the specific volume formula (UNESCO, 1987) at 1 atm within 1.6E-10 m3 kg-1, with the specific heat formula (UNESCO, 1983) at 1 atm within 0.012 J kg-1 K-1, with the sound speed formula (UNESCO, 1983) within 0.015 m s-1, with dilution heat data of MILLERO, HANSEN and HOFF (1973) at 25 and 30-degrees-C within 7.3 J mol-1 and with the osmotic coefficient formula of MILLERO and LEUNG (1976) at 0-degrees-C within 0.07 J kg-1 in specific free enthalpy. For exact computation the thermodynamic potential G is given by 81 double precision coefficients. An additional polynomial for calculation of potential temperatures for arbitrary reference pressures is derived by temperature-entropy inversion consistent with G(S, t, p) within 0.00005-degrees-C. Based on the full internal mathematical consistency of all functions derived from G(S, t, p), various quantities like enthalpy, entropy, internal energy, chemical potential etc. are tabulated as functions of salinity, temperature and pressure. Because of the polynomial structure of the new thermodynamic potential, partial derivatives are very effectively done on a computer by index shifting of the coefficient matrix.
