A calculation of relative humidity with a change of temperature using JavaScript. Also calculates the dew point and the vapor pressure.

Enter the first temperature and relative humidity, along with the second temperature, below. Press the calculate button, and the relative humidity at the second temperature is displayed. The absolute humidity (measured in mm Hg) is also displayed, along with the dew point (the temperature at which the relative humidity is 100%).

The calculation is performed using a form of the Clausius-Clapeyron equation:

P = P

_{o}e^{-H / R T}

where P is the saturated water vapor pressure, P_{o} is a
pre-exponential factor (1.11 x 10^{9} mm Hg, equivalent to
the vapor pressure of water at infinite temperature), H is the
enthalpy of evaporation (43.8 kJ/mol), R is the gas constant
(8.314 J/Kmol) and T is the absolute temperature (in K). P_{o}
and H were chosen so that the equation fits two data points
exactly; 23.76 mm Hg at 25 C and 31.80 mm Hg at 30 C.

Knowing the saturated water vapor pressure, which is only
dependent upon temperature, the absolute water vapor pressure is
calculated directly using the relative humidity. To calculate the
relative humidity at a second temperature, the saturated water
vapor pressure is again calculated, and the original absolute
vapor is divided by this number. To calculate the dewpoint, the
Clausius-Clapeyron equation is solved for temperature, and the
absolute humidity

is used as the independent variable.

Thanks to Psyke Phaeton for correcting the value of the
pre-exponential factor in the text above (although the Javascript
value was fine).

And no, those guys up there are not Clausius and Clapeyron.

Debut: December 14, 2009. Revision No. 2.
August 26, 2012

Other Pages by the Author. Please send comments on this page to: Jeffrey Clymer