Psychrometric constant

The psychrometric constant ${\displaystyle \gamma }${\displaystyle \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.^[1]

${\displaystyle \gamma ={\frac {\left(c_{p}\right)_{air}*P}{\lambda _{v}*MW_{ratio}}}}${\displaystyle \gamma ={\frac {\left(c_{p}\right)_{air}*P}{\lambda _{v}*MW_{ratio}}}}

${\displaystyle \gamma =}${\displaystyle \gamma =} psychrometric constant [kPa °C⁻¹],

P = atmospheric pressure [kPa],

${\displaystyle \lambda _{v}=}${\displaystyle \lambda _{v}=} latent heat of water vaporization, 2.45 [MJ kg⁻¹],

${\displaystyle c_{p}=}${\displaystyle c_{p}=} specific heat of air at constant pressure, [MJ kg⁻¹ °C⁻¹],

${\displaystyle MW_{ratio}=}${\displaystyle MW_{ratio}=} ratio molecular weight of water vapor/dry air = 0.622.

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

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

Saturated vapor pressure, ${\displaystyle e_{s}=e\left[T_{wet}\right]}${\displaystyle e_{s}=e\left[T_{wet}\right]}
Actual vapor pressure, ${\displaystyle e_{a}=e_{s}-\gamma *\left(T_{dry}-T_{wet}\right)}${\displaystyle e_{a}=e_{s}-\gamma *\left(T_{dry}-T_{wet}\right)}

here e[T] is vapor pressure as a function of temperature, T.

T_dew = the dewpoint temperature at which water condenses.

T_wet = the temperature of a wet thermometer bulb from which water can evaporate to air.

T_dry = the temperature of a dry thermometer bulb in air.

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