Wet-bulb temperature

Thermodynamic wet-bulb temperature

The thermodynamic wet-bulb temperature is the temperature a volume of air would have if cooled adiabatically to saturation by evaporation of water into it, all latent heat being supplied by the volume of air.

The temperature of an air sample that has passed over a large surface of liquid water in an insulated channel is the thermodynamic wet-bulb temperature—the air has become saturated by passing through a constant-pressure, ideal, adiabatic saturation chamber.

Meteorologists and others may use the term "isobaric wet-bulb temperature" to refer to the "thermodynamic wet-bulb temperature". It is also called the "adiabatic saturation temperature", though meteorologists also use "adiabatic saturation temperature" to mean "temperature at the saturation level", i.e. the temperature the parcel would achieve if it expanded adiabatically until saturated.

The thermodynamic wet-bulb temperature is a thermodynamic property of a mixture of air and water vapor. The value indicated by a simple wet-bulb thermometer often provides an adequate approximation of the thermodynamic wet-bulb temperature.

For an accurate wet-bulb thermometer, "the wet-bulb temperature and the adiabatic saturation temperature are approximately equal for air-water vapor mixtures at atmospheric temperature and pressure. This is not necessarily true at temperatures and pressures that deviate significantly from ordinary atmospheric conditions, or for other gas–vapor mixtures."

Temperature reading of wet-bulb thermometer

Wet-bulb temperature is measured using a thermometer that has its bulb wrapped in cloth—called a sock—that is kept wet with distilled water via wicking action. Such an instrument is called a wet-bulb thermometer. A widely used device for measuring wet- and dry-bulb temperature is a sling psychrometer, which consists of a pair of mercury bulb thermometers, one with a wet "sock" to measure the wet-bulb temperature and the other with the bulb exposed and dry for the dry-bulb temperature. The thermometers are attached to a swivelling handle, which allows them to be whirled around so that water evaporates from the sock and cools the wet bulb until it reaches thermal equilibrium.

An actual wet-bulb thermometer reads a temperature that is slightly different from the thermodynamic wet-bulb temperature, but they are very close in value. This is due to a coincidence: for a water-air system the psychrometric ratio (see below) happens to be close to 1, although for systems other than air and water they might not be close.

To understand why this is so, first consider the calculation of the thermodynamic wet-bulb temperature.

Experiment 1

In this case, a stream of unsaturated air is cooled. The heat from cooling that air is used to evaporate some water which increases the humidity of the air. At some point the air becomes saturated with water vapor (and has cooled to the thermodynamic wet-bulb temperature). In this case we can write the following balance of energy per mass of dry air:

$${\displaystyle (H_{\mathrm{s}\mathrm{a}\mathrm{t}}-H_0)\cdot \lambda =(T_0-T_{\mathrm{s}\mathrm{a}\mathrm{t}})\cdot c_{\mathrm{s}}}$$

• ${\displaystyle H_{\mathrm{s}\mathrm{a}\mathrm{t}}}$ saturated water content of the air (kg_H2O/kg_{dry air})
• ${\displaystyle H_0}$ initial water content of the air (same unit as above)
• ${\displaystyle \lambda }$ latent heat of water (J/kg_H2O)
• ${\displaystyle T_0}$ initial air temperature (K)
• ${\displaystyle T_{\mathrm{s}\mathrm{a}\mathrm{t}}}$ saturated air temperature (K)
• ${\displaystyle c_s}$ specific heat of air (J/kg·K)

Experiment 2

For the case of the wet-bulb thermometer, imagine a drop of water with unsaturated air blowing over it. As long as the vapor pressure of water in the drop (function of its temperature) is greater than the partial pressure of water vapor in the air stream, evaporation will take place. Initially, the heat required for the evaporation will come from the drop itself.

Instead, as the drop starts cooling, it is now colder than the air, so convective heat transfer begins to occur from the air to the drop. Furthermore, the evaporation rate depends on the difference of concentration of water vapor between the drop-stream interface and the distant stream (i.e. the "original" stream, unaffected by the drop), and on a convective mass transfer coefficient, which is a function of the components of the mixture (i.e. water and air).

After a certain period, an equilibrium is reached: the drop has cooled to a point where the rate of heat carried away in evaporation is equal to the heat gain through convection. At this point, the following balance of energy per interface area is true:

$${\displaystyle (H_{\mathrm{s}\mathrm{a}\mathrm{t}}-H_0)\cdot \lambda \cdot k^{\prime }=(T_0-T_{\mathrm{e}\mathrm{q}})\cdot h_{\mathrm{c}}}$$

• ${\displaystyle H_{\mathrm{s}\mathrm{a}\mathrm{t}}}$ water content of interface at equilibrium (kg_H2O/kg_{dry air}) (note that the air in this region is and has always been saturated)
• ${\displaystyle H_0}$ water content of the distant air (same unit as above)
• ${\displaystyle k^{\prime }}$ mass transfer coefficient (kg/m²⋅s)
• ${\displaystyle T_0}$ air temperature at distance (K)
• ${\displaystyle T_{\mathrm{e}\mathrm{q}}}$ water drop temperature at equilibrium (K)
• ${\displaystyle h_{\mathrm{c}}}$ convective heat transfer coefficient (W/m²·K)

Note that:

• ${\displaystyle (H-H_0)}$ is the driving force for mass transfer (constantly equal to ${\displaystyle H_{\mathrm{s}\mathrm{a}\mathrm{t}}-H_0}$ throughout the entire experiment)
• ${\displaystyle (T_0-T)}$ is the driving force for heat transfer (when ${\displaystyle T}$ reaches ${\displaystyle T_{\mathrm{e}\mathrm{q}}}$, the equilibrium is reached)

Let us rearrange that equation into:

$${\displaystyle (H_{\mathrm{s}\mathrm{a}\mathrm{t}}-H_0)\cdot \lambda =(T_0-T_{\mathrm{e}\mathrm{q}})\cdot \frac{h_{\mathrm{c}}}{k^{\prime }}}$$

Now let's go back to our original "thermodynamic wet-bulb" experiment, Experiment 1. If the air stream is the same in both experiments (i.e. ${\displaystyle H_0}$ and ${\displaystyle T_0}$ are the same), then we can equate the right-hand sides of both equations:

$${\displaystyle (T_0-T_{\mathrm{s}\mathrm{a}\mathrm{t}})\cdot c_{\mathrm{s}}=(T_0-T_{\mathrm{e}\mathrm{q}})\cdot \frac{h_{\mathrm{c}}}{k^{\prime }}}$$

Rearranging:

$${\displaystyle T_0-T_{\mathrm{s}\mathrm{a}\mathrm{t}}=(T_0-T_{\mathrm{e}\mathrm{q}})\cdot \frac{h_{\mathrm{c}}}{k^{\prime }\cdot c_{\mathrm{s}}}}$$

If ${\displaystyle {\displaystyle \frac{h_{\mathrm{c}}}{k^{\prime }{c}_{\mathrm{s}}}}=1}$ then the temperature of the drop in Experiment 2 is the same as the wet-bulb temperature in Experiment 1. Due to a coincidence, for the mixture of air and water vapor this is the case, the ratio (called psychrometric ratio) being close to 1.

Experiment 2 is what happens in a common wet-bulb thermometer, meaning that its reading is fairly close to the thermodynamic ("real") wet-bulb temperature.

Experimentally, the wet-bulb thermometer reads closest to the thermodynamic wet-bulb temperature if:

• The sock is shielded from radiant heat exchange with its surroundings
• Air flows past the sock quickly enough to prevent evaporated moisture from affecting evaporation from the sock
• The water supplied to the sock is at the same temperature as the thermodynamic wet-bulb temperature of the air

In practice the value reported by a wet-bulb thermometer differs slightly from the thermodynamic wet-bulb temperature because:

• The sock is not perfectly shielded from radiant heat exchange
• Air flow rate past the sock may be less than optimum
• The temperature of the water supplied to the sock is not controlled

At relative humidities below 100 percent, water evaporates from the bulb, cooling it below ambient temperature. To determine relative humidity, ambient temperature is measured using an ordinary thermometer, better known in this context as a dry-bulb thermometer. At any given ambient temperature, less relative humidity results in a greater difference between the dry-bulb and wet-bulb temperatures; the wet-bulb is colder. The precise relative humidity is determined by reading from a psychrometric chart of wet-bulb versus dry-bulb temperatures, or by calculation.

Psychrometers are instruments with both a wet-bulb and a dry-bulb thermometer.

A wet-bulb thermometer can also be used outdoors in sunlight in combination with a globe thermometer (which measures the incident radiant temperature) to calculate the wet-bulb globe temperature (WBGT).

Adiabatic wet-bulb temperature

The adiabatic wet-bulb temperature is the temperature a volume of air would have if cooled adiabatically to saturation and then compressed adiabatically to the original pressure in a moist-adiabatic process. Such cooling may occur as air pressure reduces with altitude, as noted in the article on lifted condensation level.

This term, as defined in this article, may be most prevalent in meteorology.

As the value referred to as "thermodynamic wet-bulb temperature" is also achieved via an adiabatic process, some engineers and others may use the term "adiabatic wet-bulb temperature" to refer to the "thermodynamic wet-bulb temperature". As mentioned above, meteorologists and others may use the term "isobaric wet-bulb temperature" to refer to the "thermodynamic wet-bulb temperature".

"The relationship between the isobaric and adiabatic processes is quite obscure. Comparisons indicate, however, that the two temperatures are rarely different by more than a few tenths of a degree Celsius, and the adiabatic version is always the smaller of the two for unsaturated air. Since the difference is so small, it is usually neglected in practice."

Wet-bulb depression

The wet-bulb depression is the difference between the dry-bulb temperature and the wet-bulb temperature. If there is 100% humidity, dry-bulb and wet-bulb temperatures are identical, making the wet-bulb depression equal to zero in such conditions.

Wet-bulb temperature and health

Living organisms can survive only within a certain temperature range. When the ambient temperature is excessive, many animals cool themselves to below ambient temperature by evaporative cooling (sweat in humans and horses, saliva and water in dogs and other mammals); this helps to prevent potentially fatal hyperthermia due to heat stress. The effectiveness of evaporative cooling depends upon humidity; wet-bulb temperature, or more complex calculated quantities such as wet-bulb globe temperature (WBGT) which also takes account of solar radiation, give a useful indication of the degree of heat stress, and are used by several agencies as the basis for heat stress prevention guidelines.

Given the body's vital requirement to maintain a core temperature of approximately 37 °C (99 °F), a sustained wet-bulb temperature exceeding 35 °C (95 °F)—equivalent to a heat index of 71 °C (160 °F)— is likely to be fatal even to fit and healthy people, semi-nude in the shade and next to a fan; at this temperature human bodies switch from shedding heat to the environment, to gaining heat from it. A 2022 study found that the critical wet-bulb temperature at which heat stress can no longer be compensated in young, healthy adults mimicking basic activities of daily life strongly depended on the ambient temperature and humidity conditions, but was 5–10 °C (9–18 °F) below the theoretical limit.

A 2015 study concluded that depending on the extent of future global warming, parts of the world may become uninhabitable due to deadly wet-bulb temperatures as early as 2045. A 2020 study reported cases where a 35 °C (95 °F) wet-bulb temperature had already occurred, albeit too briefly and in too small a locality to cause fatalities. Severe mortality and morbidity impacts can occur at much lower wet-bulb temperatures due to suboptimal physiological and behavioral conditions; the 2003 European and 2010 Russian heat waves had values no greater than 28 °C (82 °F).

In 2018, South Carolina implemented new regulations to protect high school students from heat-related emergencies during outdoor activities. Specific guidelines and restrictions are in place for wet-bulb globe temperatures between 82.0 °F (27.8 °C) and 92.0 °F (33.3 °C); wet-bulb globe temperatures of 92.1 °F (33.4 °C) or greater require all outdoor activities to be canceled.

Wet-bulb temperature extremes (WTEs), as they are known, rarely exceed 2,000 square kilometers.

Heat waves with high humidity

• On 8 July 2003, Dhahran, Saudi Arabia, saw the highest heat index ever recorded at 81 °C (178 °F) with a temperature of 42 °C (108 °F) and a 35 °C (95 °F) dew point.
• The 2015 Indian heat wave saw wet-bulb temperatures in Andhra Pradesh reach 30 °C (86 °F). A similar wet-bulb temperature was reached during the 1995 Chicago heat wave.
• A heat wave in August 2015 saw temperatures of 48.6 °C (119.5 °F) and a dew point of 29.5 °C (85.1 °F) at Samawah, Iraq, and 46 °C (115 °F) with a dew point of 32 °C (90 °F) in Bandar-e Mahshahr, Iran. This implied wet-bulb temperatures of about 33.5 °C (92.3 °F) and 34.7 °C (94.5 °F) respectively. The government urged residents to stay out of the sun and drink plenty of water.

Highest recorded wet-bulb temperatures

The following locations have recorded wet-bulb temperatures of 34 °C (93 °F) or higher. (Weather stations are typically at airports, so other locations in the city may have experienced higher values.)

Climate change

Study results indicate that limiting global warming to 1.5 °C would prevent most of the tropics from reaching the wet-bulb temperature of the human physiological limit of 35 °C.