A thermodynamic potential of seawater in terms of Absolute Salinity, Conservative Temperature, and in situ pressure - T. J. McDougall; P. M. Barker; R. Feistel; F. Roquet (Ocean Science, 2023)
A thermodynamic potential is derived for seawater as a function of Conservative Temperature, Absolute Salinity and pressure. From this thermodynamic potential, all the equilibrium thermodynamic properties of seawater can be found, just as all these thermodynamic properties can be found from the TEOS-10 (the International Thermodynamic Equation of Seawater – 2010; IOC et al., 2010) Gibbs function (which is a function of in situ temperature, Absolute Salinity, and pressure). Present oceanographic practice in the Gibbs SeaWater Oceanographic Toolbox uses a polynomial expression for specific volume (and enthalpy) in terms of Conservative Temperature (as well as of Absolute Salinity and pressure), whereas the relationship between in situ temperature and Conservative Temperature is based on the Gibbs function. This mixed practice introduces (numerically small) inconsistencies and superfluous conversions between variables. The proposed thermodynamic potential of seawater, being expressed as an explicit function of Conservative Temperature, overcomes these small numerical inconsistencies, and in addition, the new approach allows for greater computational efficiency in the evaluation of sea surface temperature from Conservative Temperature. It is also shown that when using Conservative Temperature, the thermodynamic information in enthalpy is independent of that contained in entropy. This contrasts with the cases where either in situ temperature or potential temperature is used. In these cases, a single thermodynamic potential serves the important purpose of avoiding having to impose a separate consistency requirement between the functional forms of enthalpy and entropy.