Wet-Bulb Temperature

Wet-bulb temperature ($t_{wb}$) is the equilibrium temperature reached by a water-wetted surface as water evaporates from it into the surrounding air at constant pressure.

Physical principle

As water evaporates, it draws latent heat from the surface, cooling it. Equilibrium is reached when the heat supplied from the air (by conduction and convection) equals the heat removed by evaporation. That equilibrium temperature is $t_{wb}$.

Relation to other temperatures

$t_{wb}$ ≤ $t$ (dry-bulb temperature)
$t_{wb}$ ≥ $t_d$ (dew point)

Equality $t_{wb}$ = $t_d$ occurs at φ = 100 % (saturated air).

Psychrometric equation

Partial vapor pressure from two thermometers (Sprung’s relation):

$$p_w = p_{ws}(t_{wb}) - A \cdot p \cdot (t - t_{wb})$$

where:

• $p_{ws}$($t_{wb}$) — saturation vapor pressure at $t_{wb}$ [Pa]
• $A \approx 6.62 \times 10^{-4}\ \text{K}^{-1}$ — psychrometer coefficient (for an aspirated Assmann-type psychrometer)
• $p$ — barometric pressure [Pa]
• $t$ — dry-bulb temperature [°C]

The humidity ratio then follows from $x = 0.622 \cdot \dfrac{p_w}{p - p_w}$.

Practical applications

Evaporative cooling:
Air can be cooled at most to $t_{wb}$. Evaporative-cooler effectiveness $\eta = \dfrac{t_1 - t_2}{t_1 - t_{wb}}$.

Cooling tower:
The minimum leaving water temperature approaches the $t_{wb}$ of the ambient air (the approach temperature).

WBGT index (Wet-Bulb Globe Temperature):
Combines $t_{wb}$, the globe temperature and the dry-bulb temperature — standard ISO 7243 for assessing heat stress on workers.

Measurement

An aspirated Assmann-type psychrometer (a fan draws air past the dry and wet sensors in shielded tubes), or a capacitive temperature/humidity sensor with $t_{wb}$ computed in software.