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## Summary

The psychrometric constant $\gamma$ relates the partial pressure of water in air to the air temperature. This lets one interpolate actual vapor pressure from paired dry and wet thermometer bulb temperature readings.

$\gamma ={\frac {\left(c_{p}\right)_{air}*P}{\lambda _{v}*MW_{ratio}}}$ $\gamma =$ psychrometric constant [kPa °C−1],
P = atmospheric pressure [kPa],
$\lambda _{v}=$ latent heat of water vaporization, 2.26 [MJ kg−1],
$c_{p}=$ specific heat of air at constant pressure, [MJ kg−1 °C−1],
$MW_{ratio}=$ ratio molecular weight of water vapor/dry air = 0.622.

Both $\lambda _{v}$ and $MW_{ratio}$ are constants.
Since atmospheric pressure, P, depends upon altitude, so does $\gamma$ .
At higher altitude water evaporates and boils at lower temperature.

Although $\left(c_{p}\right)_{H_{2}O}$ is constant, varied air composition results in varied $\left(c_{p}\right)_{air}$ .

Thus on average, at a given location or altitude, the psychrometric constant is approximately constant. Still, it is worth remembering that weather impacts both atmospheric pressure and composition.

## Vapor Pressure Estimation

Saturated vapor pressure, $e_{s}=e\left[T_{wet}\right]$ Actual vapor pressure, $e_{a}=e_{s}-\gamma *\left(T_{dry}-T_{wet}\right)$ here e[T] is vapor pressure as a function of temperature, T.
Tdew = the dewpoint temperature at which water condenses.
Twet = the temperature of a wet thermometer bulb from which water can evaporate to air.
Tdry = the temperature of a dry thermometer bulb in air.