Abstract
AbstractWe present and assess a simple equation for saturated vapour pressure over water and ice. The equation does not rely on an explicit integration of the Clausius–Clapeyron equation, but instead uses the equality of the Gibbs functions of the vapour and the liquid or ice in equilibrium. The resulting equation is simple, physically consistent with standard thermodynamic assumptions, uses only basic physical parameters, and is at least as accurate as commonly used empirical fits. It is further shown that the finite volume of liquid water has a negligible effect on the vapour pressure. The main variation from accurate tabulated data results from the variation of vapour and liquid isobaric heat capacities. Nevertheless, it is shown that, for the purpose of accurate calculation of saturated vapour pressure, this can usually be ignored.
Highlights
The common way of calculating the saturated vapour pressure over a liquid is to integrate the Clausius–Clapeyron equation
We present and assess a simple equation for saturated vapour pressure over water and ice
This equation results from equating the Gibbs functions of the liquid and the vapour—a requirement for thermodynamic equilibrium—and demanding that any variation of the vapour Gibbs function with temperature and pressure must equal the variation in the liquid Gibbs function, as in, for example, Ambaum (2010)
Summary
The common way of calculating the saturated vapour pressure over a liquid is to integrate the Clausius–Clapeyron equation This equation results from equating the Gibbs functions of the liquid and the vapour—a requirement for thermodynamic equilibrium—and demanding that any variation of the vapour Gibbs function with temperature and pressure must equal the variation in the liquid Gibbs function, as in, for example, Ambaum (2010). Because the expression is derived directly from normally assumed thermodynamic properties of air and water, it is consistent with those assumptions, contrary to empirical fits. This approach ties in closely with recent developments describing atmospheric thermodynamics based on Gibbs functions in, for example, Thuburn (2017).
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