Thermodynamic properties of seawater, ice and humid air: TEOS-10, before and beyond

Abstract

Abstract. In the terrestrial climate system, water is a key player in the form of its different ambient phases of ice, liquid and vapour, admixed with sea salt in the ocean and with dry air in the atmosphere. For proper balances of climatic energy and entropy fluxes in models and observations, a highly accurate, consistent and comprehensive thermodynamic standard framework is requisite in geophysics and climate research. The new Thermodynamic Equation of Seawater -2010 (TEOS-10) constitutes such a standard for properties of water in its various manifestations in the hydrological cycle.

Distinguishing between Clausius, Boltzmann and Pauling Entropies of Frozen Non-Equilibrium States

“…At low temperatures, typically about 10 K, thermal energy falls below the finite excitation energy of other quantum states, and the cubic law starts dominating the heat capacity. For example, the reference equation of state for hexagonal ice (Feistel and Wagner [ 75 , 76 , 77 , 78 ], Feistel [ 18 ]) obeys those Debye [ 74 ] and Grüneisen [ 79 ] laws, consistently with experimental data. For amorphous solids, the transition temperature may be even lower (Gutzow and Schmelzer [ 5 ], p. 209).…”

“…Equation (4) serves as the definition of Clausius entropy in this paper. Note that definitions formally deviating from Equation (4) may be considered elsewhere for certain reasons, such as specifying T ref in Equation (2) by the triple point of water in order to reduce the uncertainty of empirical equations (Feistel [ 18 ]), or by the melting temperature of metastable, glass-like solids. Such arbitrary definitions, if deviating from Equation (4) by merely a numerical constant, do neither affect any measurable thermodynamic properties nor the physical description of natural processes.…”

“… Specific dilution enthalpy of ocean surface water when admixed with freshwater (rain, melting ice, river discharge) for different freshwater fractions, w , and temperatures in °C as indicated by the curves (Feistel [ 35 ]). Diagram computed from the TEOS-10 Gibbs function of seawater (Feistel [ 18 , 36 ]). …”

“…appear in the related equations. For this reason, international standard equations for thermodynamic properties of water, seawater, ice or humid air are expressed in entropies that formally vanish at experimentally convenient reference points at which the measurement uncertainty is sufficiently small, such as the triple point of water, rather than at T = 0 (Feistel [ 18 ]). The convenient technical setting of the value for the zero-point entropy is consistent with all available reliable thermodynamic measurements and is in no way related to the fact that “the general theoretical proof of the fact that the state of a system with the smallest energy is at the same time one of zero entropy has not yet been given” (Simon [ 39 ]).…”

“…This means that the system’s volume may be divided into spatial cells that are sufficiently small (but still macroscopic) so that each cell can reasonably be assumed to be in internal equilibrium, while not necessarily being in mutual equilibria with adjacent cells. For non-equilibrium systems in local equilibrium, such as a solid exhibiting a temperature gradient, thermodynamic properties remain well-defined and measurable locally (Glansdorff and Prigogine [ 13 ], Falkenhagen and Ebeling [ 14 ], Subarew [ 15 ], Ebeling and Feistel [ 16 ], De Groot and Mazur [ 17 ], Feistel [ 18 ]). Restrictions to local equilibrium permit the easy use of temperature and entropy as thermodynamic properties.…”