Activity of Supercooled Water on the Ice Curve and Other Thermodynamic Properties of Liquid Water up to the Boiling Point at Standard Pressure

Abstract

A simple model for thermodynamic properties of water from subzero temperatures up to 373 K was derived at ambient pressure. The heat capacity of supercooled water was assessed as lambda transition. The obtained properties for supercooled water such as heat capacity, vapor pressure, density and thermal expansion are in excellent agreement with literature data. Activity of water on ice curve, independent of used electrolyte and Debye-Hückel constant applied in modeling, is also calculated. Thus, the ice curve activity of supercooled water can be used as a universal basis for thermodynamic modeling of aqueous solutions, precipitating hydrated and anhydrous solids. A simple model for heat capacity, density and thermal expansion of ice are also derived from 170 K up to melting point.

Figure 1

Assessed heat capacity C_p of supercooled water (line) as a function of temperature compared with experimental data^,,, (dots) at subzero temperatures. Dashed line presents extrapolated values. Equation used in freezing point modeling by Thomsen et al. is also shown in the graph.

Figure 2

Assessed heat capacity C_p of solid ice (black line) as a function of temperature compared with experimental data^, (dots) and equations in the literature^, (red and blue lines).

Figure 3

Assessed heat capacity change, ΔC_p^°, as a function of temperature compared with the equation of Thurmond and Brass.

Figure 4

Assessed density ρ of liquid water compared with experimental data.^,,, Dotted lines indicate extrapolated values. Data by Speedy and Lind and Trusler were not included in the assessment.

Figure 5

Calculated molar volume ν of liquid water compared with literature data.^,,

Figure 6

Calculated thermal expansion coefficient of liquid water compared with the literature values.^,,,

Figure 7

Assessed density ρ of solid ice compared with the model of Feistel and Wagner.

Figure 8

Calculated molar volume difference Δν = ν_w – ν_ice between supercooled water and solid ice.

Figure 9

Vapor pressure of ice p_ice according to various authors.^,−

Figure 10

Calculated vapor pressure of pure supercooled water p_w compared with selected literature data.^,− Not all data by Kraus and Greer is shown on the graph.

Figure 11

Calculated vapor pressure difference Δp = p_w – p_ice between pure supercooled water and ice compared with the literature data.^,

Figure 12

Difference in calculated vapor pressure of pure supercooled water, Δp = p_thiswork – p_Koop, compared with the equation presented by Murphy and Koop. The diamonds (blue) were calculated with eq 25 and squares (red) with eq 23.

Figure 13

Calculated activity of supercooled water on ice curve compared to activity using eq 10 to equilibrium constants by Murphy and Koop and Spencer et al. as well as polynomial equation with six terms by Carslaw et al. and Toner et al.