# How does a change in temperature affect relative humidity

Assume that the air pressure and the amount of water in the air stay constant. How can I figure out how much a change in temperature affects the relative humidity?

• Not sure why I can't add an answer. I came up with this formula: RH1 = pH2O*(t0) / pH2O*(t1) * t0/t1 * RH0, where RH1 is the new rel. humidity, RH0 is the old one, t0 and t1 are the temperatures, and pH2O*(t) is the equilibrium vapor pressure of water at temperature t. pH2O*(t) is defined as exp(20.386 - 5132 / t), but there are alternative formulations. All temperatures are in K, pressures are in mmHg. – Erik Allik Jan 15 '16 at 12:32

## 2 Answers

Relative humidity equals actual water vapor pressure divided by saturated water vapor pressure. As temperature goes up, saturated vapor pressure goes up as well, and relative humidity will go down, if absolute humidity remains the same. The exact relationship must be measured.

Relative humidity is just the percentage of what the air at a given temperature can hold. This is given by the Clausius–Clapeyron equation, which rises roughly exponentially with temperature doubling approx every 10degrees C. So if your relative humidity is X, and the saturation vapor pressure at the new temperature is Y times the value at the old temperature, your new (constant volume) humidity is X/Y. You wanted constant pressure, so your absolute humidity is changed by the change in volume, i.e. your humidity also scales inversely with volume, although this second effect is much smaller than the first.

• Actually the "can hold" can more accurately be understood as there is a rate for water vapor condensing, and another rate for droplets evaporating. The dew point is the temperature at which these rates are equal. Dew Point That means it does not actually depend on other gas, such as air, being present. – Mike Dunlavey Oct 5 '11 at 19:55
• The relative humidity is the ratio of the partial vapor pressure over the equilibrium vapor pressure. Do you actually mean to say the ratio (relative humidity) rather than the pressure (equilibrium vapor pressure) itself is given by the Clausius-Clapeyron equation? – Hans Jun 4 '17 at 23:43

## protected by ACuriousMind♦Oct 22 '15 at 2:14

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