Wet-bulb temperature

Humidity and hygrometry

Specific concepts
Absolute / Specific / Relative Dew point (depression) Psychrometrics
General concepts
Air Concentration Density Dew Evaporation Humidity buffering (Atm.) Pressure Liquid water Avogadro's law Nucleation Thermodynamic equilibrium
Measures and Instruments
Heat index Sat. vap. density Mixing ratio Water activity H. indicator card Hygrometer Dry/Wet-bulb temperature

The wet-bulb temperature is the temperature a parcel of air would have if it were cooled to saturation (100% relative humidity) by the evaporation of water into it, with the latent heat being supplied by the parcel.^[1] A wet-bulb thermometer will indicate a temperature close to the true (thermodynamic) wet-bulb temperature. The wet-bulb temperature is the lowest temperature that can be reached under current ambient conditions by the evaporation of water only. Wet-bulb temperature is largely determined by both actual air temperature (dry-bulb temperature) and the amount of moisture in the air (humidity). At 100% relative humidity, the wet-bulb temperature equals the dry-bulb temperature.

General

The thermodynamic wet-bulb temperature is the lowest temperature which may be achieved by evaporative cooling of a water-wetted (or even ice-covered), ventilated surface.

By contrast, the dew point is the temperature to which the ambient air must be cooled to reach 100% relative humidity assuming there is no evaporation into the air; it is the point where condensate (dew) and rain would form.

For a parcel of air that is less than saturated (i.e., air with less than 100 percent relative humidity), the wet-bulb temperature is lower than the dry-bulb temperature, but higher than the dew point temperature. The lower the relative humidity (the drier the air), the greater the gaps between each pair of these three temperatures. Conversely, when the relative humidity rises to 100%, the three figures coincide.

For air at a known pressure and dry-bulb temperature, the thermodynamic wet-bulb temperature corresponds to unique values of the relative humidity and the dew point temperature. It therefore may be used for the practical determination of these values. The relationships between these values are illustrated in a psychrometric chart.

Cooling of the human body through perspiration is inhibited as the wet-bulb temperature (and absolute humidity) of the surrounding air increases in summer. Other mechanisms may be at work in winter if there is validity to the notion of a "humid" or "damp cold."

Lower wet-bulb temperatures that correspond with drier air in summer can translate to energy savings in air-conditioned buildings due to:

Reduced dehumidification load for ventilation air
Increased efficiency of cooling towers

Thermodynamic wet-bulb temperature (adiabatic saturation 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 called 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 it should be pointed out that 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.^[2]

Thermodynamic wet-bulb temperature is plotted on a psychrometric chart.

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."^[3]

Temperature reading of wet-bulb thermometer

A Wet Dry Hygrometer featuring a wet-bulb thermometer

A sling psychrometer. The sock is wet with distilled water and whirled around for a minute or more before taking the readings.

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 vapour (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:

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

$H_\mathrm{sat}$ saturated water content of the air (kg_H2O/kg_{dry air})
$H_0$ initial water content of the air (same unit as above)
$\lambda$ latent heat of water (J/kg_H2O)
$T_0$ initial air temperature (K)
$T_\mathrm{sat}$ saturated air temperature (K)
$c_s$ 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 since the fastest moving water molecules are most likely to escape the surface of the drop, so the remaining water molecules will have a lower average speed and therefore a lower temperature. If this were the only thing that happened and the air started bone dry, if the air blew sufficiently fast then its partial pressure of water vapor would remain constantly zero and the drop would get infinitely cold.

Clearly this doesn't happen. It turns out that, as the drop starts cooling, it's now colder than the air, so convective heat transfer begins to occur from the air to the drop. Also, understand that 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:

$(H_\mathrm{sat} - H_0) \cdot \lambda \cdot k' = (T_0 - T_\mathrm{eq}) \cdot h_\mathrm{c}$

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

Note that:

$(H - H_0)$ is the driving force for mass transfer (constantly equal to $H_\mathrm{sat} - H_0$ throughout the entire experiment)
$(T_0 - T)$ is the driving force for heat transfer (when $T$ reaches $T_\mathrm{eq}$ , the equilibrium is reached)

Let us rearrange that equation into:

$(H_\mathrm{sat} - H_0) \cdot \lambda = (T_0 - T_\mathrm{eq}) \cdot \frac{h_\mathrm{c}}{k'}$

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. $H_0$ and $T_0$ are the same), then we can equate the right-hand sides of both equations:

$(T_0 - T_\mathrm{sat}) \cdot c_\mathrm{s} = (T_0 - T_\mathrm{eq}) \cdot \frac{h_\mathrm{c}}{k'}$

Rearranging a little bit:

$T_0 - T_\mathrm{sat} = (T_0 - T_\mathrm{eq}) \cdot \frac{h_\mathrm{c}}{k' \cdot c_\mathrm{s}}$

It is clear now that if $\dfrac{h_\mathrm{c}}{k' c_\mathrm{s}} = 1$ 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.^[4]

Experiment 2 is what happens in a common wet-bulb thermometer. That's why 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 which cools the bulb 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 (AMS Glossary). 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."^[5]

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.^[6]

Wet-bulb temperature and health

Living organisms can survive only within a certain temperature range. When the ambient temperature is excessive, humans and many animals cool themselves below ambient by evaporative cooling of sweat (or other aqueous liquid; saliva in dogs, for example); 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.

A sustained wet-bulb temperature exceeding 35 °C (95 °F) is likely to be fatal even to fit and healthy people, unclothed in the shade next to a fan; at this temperature our bodies switch from shedding heat to the environment, to gaining heat from it.^[7] Thus 35 °C is the threshold beyond which the body is no longer able to adequately cool itself. A study by NOAA from 2013 concluded that heat stress will reduce labor capacity considerably under current emissions scenarios.^[8]

A 2010 study by Purdue University concluded that under a worst case scenario for global warming, the wet-bulb temperature limit for humans could be exceeded around much of the world in future centuries.^[9] A 2015 study concluded that parts of the globe could become uninhabitable.^[10] An example of the threshold at which the human body is no longer able to cool itself and begins to overheat is a humidity level of 50% and a high heat of 46 °C (115 °F), as this would indicate a wet-bulb temperature of 35 °C (95 °F).^[11]

References

↑ A Dictionary of Weather. Oxford Reference. ISBN 978-0-19-954144-7.
↑ http://amsglossary.allenpress.com/glossary/search?p=1&query=adiabatic+saturation+temperature&submit=Search [AMS Glossary]
↑ VanWylen, Gordon J; Sonntag, Richard E. (1973). Fundamentals of Classical Thermodynamics (2nd ed.). Wiley. p. 448. ISBN 0471902276.
↑ accessed 20080408
↑ NWSTC Remote Training Module; SKEW T LOG P DIAGRAM AND SOUNDING ANALYSIS; RTM - 230; National Weather Service Training Center; Kansas City, MO 64153; July 31, 2000
↑ Dry Bulb, Wet Bulb and Dew Point Temperature
↑ Sherwood, S.C.; Huber, M. (25 May 2010). "An adaptability limit to climate change due to heat stress". Proc. Natl. Acad. Sci. U.S.A. 107 (21): 9552–5. doi:10.1073/pnas.0913352107. PMID 20439769.
↑ Dunne, John P.; Stouffer, Ronald J.; John, Jasmin G. (2013). "Heat stress reduces labor capacity under climate warming". Geophysical Fluid Dynamics Laboratory. Bibcode:2013NatCC...3..563D. doi:10.1038/nclimate1827.
↑ "Researchers find future temperatures could exceed livable limits". Purdue University. May 4, 2010.
↑ Jeremy S. Pal & Elfatih A. B. Eltahir (2015). "Future temperature in southwest Asia projected to exceed a threshold for human adaptability". Nature. doi:10.1038/nclimate2833.
↑ "Persian Gulf could be too hot for humans by 2100; Global warming could make areas of the Persian Gulf uninhabitable to humans in less than 10 years, a study has claimed". AFP. The Daily Telegraph. 26 October 2015. Retrieved 27 October 2015.

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