Accurate Expressions for the Dewpoint and Frost Point Derived from the Rankine-Kirchhoff Approximations

Accurate, explicit, and analytic expressions are derived for the dewpoint and frost point as functions of temperature and relative humidity. These are derived theoretically in terms of physical constants using the Rankine-Kirchhoff approximations, which assume an ideal gas, fixed heat capacities, and zero specific volume of condensates. Compared to modern laboratory measurements, the expressions are accurate to within a few hundredths of a degree over the full range of Earth-relevant temperatures, from 180 to 273K for the frost point and 230 to 330K for the dewpoint.

Automated summary

Accurate and explicit expressions for dewpoint and frost point as functions of temperature and relative humidity have been derived theoretically using physical constants and Rankine-Kirchhoff approximations. Compared to modern laboratory measurements, these expressions are accurate to within a few hundredths of a degree over the full range of Earth-relevant temperatures.