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Temperature K °C Estimate

Symbol	Name	Value	Reference

Formula

Self-diffusion coefficient [1]

$$\begin{align*} D &= D_0 [\frac{T_K}{T_s} - 1]^{\gamma} \\ \text{where} \\ D_0 &= (1.635 \times 10^{-8} \pm 2.242 \times 10^{-11}) ~ \text{m}^2\text{s}^{-1}, \\ T_s &= (215.05 \pm 1.20) ~ \text{K}, \\ \gamma &= 2.063 \pm 0.051 \end{align*}$$

Density [2]

$$\begin{align*} \rho &= \frac{a_0 + a_1 T_C + a_2 T_C^2 + a_3 T_C^3 + a_4 T_C^4 + a_5 T_C^5}{1 + b T_C} \\ \text{where} \\ a_0 &= 999.83952, \\ a_1 &= 16.945176, \\ a_2 &= -7.9870401 \cdot 10^{-3}, \\ a_3 &= -46.170461 \cdot 10^{-6}, \\ a_4 &= 105.56302 \cdot 10^{-9}, \\ a_5 &= -280.54253 \cdot 10^{-12}, \\ b &= 16.87985 \cdot 10^{-3} \end{align*}$$

Isothermal compressibility [2]

$$\begin{align*} \beta_{T} &= \frac{a_0 + a_1 T_C + a_2 T_C^2 + a_3 T_C^3 + a_4 T_C^4 + a_5 T_C^5}{1 + b T_C} \\ \text{where} ~ (T_C < 100) \\ a_0 &= 50.88496, \\ a_1 &= 0.6163813, \\ a_2 &= 1.459187 \cdot 10^{-3}, \\ a_3 &= 20.08438 \cdot 10^{-6}, \\ a_4 &= -58.47727 \cdot 10^{-9}, \\ a_5 &= 410.4110 \cdot 10^{-12}, \\ b &= 19.67348 \cdot 10^{-3} \\ \text{or} ~ (100 < T_C < 150) \\ a_0 &= 50.884917, \\ a_1 &= 0.62590623, \\ a_2 &= 1.3848668 \cdot 10^{-3}, \\ a_3 &= 21.603427 \cdot 10^{-6}, \\ a_4 &= -72.087667 \cdot 10^{-9}, \\ a_5 &= 465.45054 \cdot 10^{-12}, \\ b &= 19.859983 \cdot 10^{-3} \end{align*}$$

Thermal expansion coefficient [2]

$$\begin{align*} \alpha_{P} &= \frac{1}{V} \frac{\partial}{\partial T_C} V \\ &= \frac{1}{\frac{M}{\rho}} \frac{\partial}{\partial T_C} \frac{M}{\rho} \\ &= \rho \frac{\partial}{\partial T_C} \frac{1}{\rho} \\ &= \rho \frac{\partial}{\partial T_C} \frac{1 + b T_C}{a_0 + a_1 T_C + a_2 T_C^2 + a_3 T_C^3 + a_4 T_C^4 + a_5 T_C^5} \\ &= \rho \frac{b}{a_0 + a_1 T_C + a_2 T_C^2 + a_3 T_C^3 + a_4 T_C^4 + a_5 T_C^5} - \frac{(b T_C + 1)(a_1 + 2 a_2 t + 3 a_3 t^2 + 4 a_4 t^3 + 5 a_5 t^4)}{(a_0 + a_1 T_C + a_2 T_C^2 + a_3 T_C^3 + a_4 T_C^4 + a_5 T_C^5)^2} \\ \text{where} \\ a_0 &= 999.83952, \\ a_1 &= 16.945176, \\ a_2 &= -7.9870401 \cdot 10^{-3}, \\ a_3 &= -46.170461 \cdot 10^{-6}, \\ a_4 &= 105.56302 \cdot 10^{-9}, \\ a_5 &= -280.54253 \cdot 10^{-12}, \\ b &= 16.87985 \cdot 10^{-3} \end{align*}$$

Specific heat [2]

$$\begin{align*} C_P &= 4.1855 (0.996185 + 0.0002874(\frac{T_C + 100}{100})^{5.26} + 0.011160 \cdot 10^{-0.036 T_C}) \end{align*}$$

Reference

1. Holz M, Heil SR, Sacco A (2000) Temperature-dependent self-diffusion coefficients of water and six selected molecular liquids for calibration in accurate 1H NMR PFG measurements. Phys Chem Chem Phys 2: 4740–4742.
2. Kell GS (1975) Density, Thermal Expansivity, and Compressibility of Liquid Water from 0" to 150°C: Correlations and Tables for Atmospheric Pressure and Saturation Reviewed and Expressed on 1968 Temperature Scale. J Chem Eng Data 20: 97–105.