Vapour pressure of ice calculated from the equations of Huang (2018)

The International Association for the Properties of Water and Steam (IAPWS, 2009) adopted a formulation based on the work of Wagner and co-workers, which provides the best fit to the authoritative experimental dataset. A key advance of this formulation is that it explicitly incorporates the temperature dependence of the latent heat of sublimation, thereby improving accuracy over a wide temperature range. The formulation was later published in detail by (Wagner et al., 2011) ensuring broader dissemination and acceptance within the scientific community.
Since then, a simpler equation to that proposed by Wagner was developed by Huang (Huang, 2018). It has a general exponential form in which the vapour pressure of the pure substance (expressed in pascals, Pa) is calculated from the temperature in degrees Celsius together with a set of empirical coefficients. The coefficients take different values depending on whether the equation is applied to the saturated vapour pressure of liquid water or to that of ice.
For liquid water, the equation is valid above 0 °C, while for ice it is valid at 0 °C and below. In both cases, the structure of the equation is similar: it relates the natural logarithm of vapour pressure to a combination of constants and the reciprocal of a temperature term, adjusted by fitted parameters.
In Huang’s formulation, the symbol t is used for temperature in degrees Celsius, while an upper-case T is reserved for temperatures in Kelvin. Using the liquid-water and ice versions of the equation, values for the vapour pressure can be tabulated and plotted as curves, as presented in the Excel workbook associated with this Figshare publication.
Although less rigorous than the official IAPWS formulation, Huang’s equation offers a computationally efficient alternative, making it particularly useful for routine modelling and cycle design in freeze-drying applications.
Huang, J. (2018) ‘A Simple Accurate Formula for Calculating Saturation Vapor Pressure of Water and Ice’, J. Appl. Meteorol. Climatol., 57(6), pp. 1265–1272. Available at: https://doi.org/https://doi.org/10.1175/JAMC-D-17-0334.1.
IAPWS (2009) Revised Release on the IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use, http://www.iapws.org. Available at: http://www.iapws.org.
Wagner, W., Riethmann, T., Feistel, R. and Harvey, A.H. (2011) ‘New Equations for the Sublimation Pressure and Melting Pressure of H2O Ice Ih’, J. Phys. Chem. Ref. Data, 40(4), p. 043103. Available at: https://doi.org/https://doi.org/10.1063/1.3657937.