Wet-bulb Temperature - Temperature Reading of Wet-bulb Thermometer

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 slightly different temperature than 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 happens to be ~1, although for systems other than air and water they might not be close.

To understand why this is, first consider the calculation of the thermodynamic wet-bulb temperature: in this case, a stream of air with less than 100% relative humidity 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 water vapour in the air becomes saturated (and has cooled to the thermodynamic wet-bulb temperature). In this case we can write the following:

where is the initial water content of the air on a mass basis, is the saturated water content of the air, is the latent heat of water, is the initial air temperature, is the saturated air temperature and is the heat capacity of the air.

For the case of the wet-bulb thermometer, imagine a drop of water with air of less than 100% relative humidity blowing over it. As long as the vapor pressure of water in the drop is more than the partial pressure of water 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, then the drop would cool until the following was true:

where is the saturation pressure of the water in the drop and is a function of the drop temperature and is the partial pressure of water in the vapor phase. If the air started bone dry and was blowing sufficiently fast then would be 0 and the drop could get infinitely cold. Clearly this doesn't happen. It turns out that as the drop cools, convective heat transfer begins to occur between the warmer air and the colder water. In addition, the evaporation does not occur instantly, but instead depends on the rate of convective mass transfer between the water and the air. At a certain point the water cools to a point where the heat carried away in evaporation is equal to the heat gain through convective heat transfer. At this point the following is true:

where is now the driving force for mass transfer, k' is the mass transfer coefficient (with English units of lb/(h⋅ft2)), is the heat transfer coefficient and is the temperature driving force.

Now if this equation is compared to the thermodynamic wet-bulb equation, we can see that if the quantity (known as the psychrometric ratio) then

Due to a coincidence, for air this is the case and the ratio is very close to 1.

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).