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The Clausius–Clapeyron equation [8]: 509 applies to vaporization of liquids where vapor follows ideal gas law using the ideal gas constant and liquid volume is neglected as being much smaller than vapor volume V. It is often used to calculate vapor pressure of a liquid.
The boiling point of water is the temperature at which the saturated vapor pressure equals the ambient pressure. Water supercooled below its normal freezing point has a higher vapor pressure than that of ice at the same temperature and is, thus, unstable. Calculations of the (saturation) vapor pressure of water are commonly used in meteorology.
where temperature T is in degrees Celsius (°C) and saturation vapor pressure P is in kilopascals (kPa). According to Monteith and Unsworth, "Values of saturation vapour pressure from Tetens' formula are within 1 Pa of exact values up to 35 °C." Murray (1967) provides Tetens' equation for temperatures below 0 °C: [3]
The Antoine equation is a class of semi-empirical correlations describing the relation between vapor pressure and temperature for pure substances. The Antoine equation is derived from the Clausius–Clapeyron relation. The equation was presented in 1888 by the French engineer Louis Charles Antoine (1825–1897). [1]
According to the American Meteorological Society Glossary of Meteorology, saturation vapor pressure properly refers to the equilibrium vapor pressure of water above a flat surface of liquid water or solid ice, and is a function only of temperature and whether the condensed phase is liquid or solid. [17]
The Clausius–Clapeyron relation shows how the water-holding capacity of the atmosphere increases by about 8% per Celsius increase in temperature. (It does not directly depend on other parameters like the pressure or density.) This water-holding capacity, or "equilibrium vapor pressure", can be approximated using the August-Roche-Magnus formula
Here is a similar formula from the 67th edition of the CRC handbook. Note that the form of this formula as given is a fit to the Clausius–Clapeyron equation, which is a good theoretical starting point for calculating saturation vapor pressures: log 10 (P) = −(0.05223)a/T + b, where P is in mmHg, T is in kelvins, a = 38324, and b = 8.8017.
Values are given in terms of temperature necessary to reach the specified pressure. Valid results within the quoted ranges from most equations are included in the table for comparison. A conversion factor is included into the original first coefficients of the equations to provide the pressure in pascals (CR2: 5.006, SMI: -0.875).