The absolute seawater entropy: Part I. Definition

TL;DR

This work defines the absolute seawater entropy $\eta_{abs}$ by augmenting the TEOS10 standard entropy with third-law absolute reference entropies for liquid water and sea salts. The author derives an explicit increment $\Delta \eta_s = (\eta_{s0}-\eta_{w0}) (S_A-S_{SO})/1000$ to convert $\eta_{std/TEOS10}$ into an absolute quantity and updates the water and sea-salt reference entropies at $0^{\circ}$C and $25^{\circ}$C using contemporary thermodynamic data. Numerical comparisons show substantial differences in magnitude and sign between Millero’s earlier formulations, TEOS10’s standard version, and the new absolute TEOS10 entropy, with the absolute formulation producing more physically consistent isentropes in $t$–$S_A$ space. The results imply that absolute entropies influence not only state variables but also turbulence, chemical equilibria, and potential temperature constructs, motivating broader adoption of an absolute-entropy framework in ocean thermodynamics and signaling the need for Part II to test these ideas against observed profiles. Overall, the paper advocates replacing arbitrary reference entropy choices with third-law-consistent values to yield a thermodynamically coherent description of seawater entropy and its governing processes, potentially impacting ocean modeling and climate studies.

Abstract

The absolute entropy of seawater is defined as an improved version of the relationship defined by Franck Millero in 1976 and 1983. The first improvements concern the complex non-linear dependence of entropy on pressure, temperature and salinity, with the use of the standard TEOS10 formulation based on a fit of the oceanic Gibbs function to more recent observations. On the other hand, more recent thermodynamic tables have been used to increase the accuracy of the Millero's salinity increment to this standard formulation, to deduce the absolute version of entropy with new values for the pure-water and sea-salts absolute reference entropies. The differences between the values of the seawater entropy calculated with the Millero and TEOS10 formulations (standard and absolute) are documented, before a more complete study shown in the second part of the paper of the absolute seawater entropy computed from observed vertical profiles and analysed surface datasets.

Figures (2)

• Figure 1: Top left: the salinity parts of the Millero's (1976-1983/blue) and TEOS10's (standard/black and absolute/red) seawater entropies plotted against the absolute salinity for three selected temperatures ($0$, $20$ and $40{}^{\circ}$C). Top right and Bottom left: two zoomed versions of this diagram for very small salinity, to show the impact of the term $x^2\:\ln(x)$ corresponding to $S_{\rm A}\:\ln(S_{\rm A})$. Bottom right: the isopycnic potential-density anomaly (solid green) lines, the standard TEOS10 entropy (dashed black) lines, and the new absolute TEOS10 entropy (solid red) lines are plotted on a classical $t-S_{\rm A}$ Temperature-Salinity diagram. The three red and black circles represent isentropic processes (see the main text).
• Figure 2: (a): The specific heat at constant pressure $c_p(T)$ for H2O (Ice-Ih) for absolute temperatures $T$ from $0$ K to $T_0=273.15$ K. (b): The absolute entropies for H2O (Ice-Ih, liquid and vapour) from $0$ K to $340$ K, with the calorimetric values $\eta_0 +\int_0^T c_p(T')\:d\ln(T')$ (solid red lines) including the Pauling-Nagle residual entropy $\eta_0 \approx 0.189$ kJ K ${}^{-1}$ kg ${}^{-1}$ at $0$ K, and the statistical values $\eta=k\:\ln(W)$ (dashed blue line) automatically taking into account the residual entropy at $0$ K and the latent heat of sublimation $L_{\rm sub}(T_0) \approx 2834.5$ kJ kg ${}^{-1}$ at $273.15$ K. The term $\delta \eta \approx 10.318-2.295 = 8.023$ kJ K ${}^{-1}$ kg ${}^{-1}$ (green arrow) is the difference between the statistical water-vapour and calorimetric Ice-Ih absolute entropies at $T_0=273.15$ K.