Understanding Temperatures in a Saturated Air-Water Vapour Mixture

Let's discuss what happens to different temperature measurements when air is saturated with water vapour. We measure air temperature in a few different ways, and in specific conditions like saturation, these measurements become related in a unique way.

What is a Saturated Air-Water Vapour Mixture?

A saturated air-water vapour mixture is air that holds the maximum amount of water vapour it possibly can at that specific temperature and pressure. It cannot absorb any more moisture.

Defining the Temperatures

• Dry Bulb Temperature (DBT): This is the standard air temperature measured by a regular thermometer. It doesn't account for the moisture content in the air.
• Wet Bulb Temperature (WBT): This temperature is measured by a thermometer with its bulb wrapped in a wet cloth and exposed to a stream of air. As water evaporates from the cloth, it cools the bulb. The amount of cooling depends on how dry the air is; drier air causes more evaporation and thus lower WBT.
• Dew Point Temperature (DPT): This is the temperature at which the air becomes saturated if it is cooled at constant pressure. Below the dew point temperature, water vapour will start condensing into liquid water (dew).

Relationship in General Conditions

In typical unsaturated air conditions, the relationship between these temperatures is usually:

DBT > WBT > DPT

This is because drier air allows for significant evaporative cooling (lowering WBT) and the air must be cooled below the WBT to reach saturation and start condensing (DPT).

Temperatures in a Saturated Mixture

Now, let's consider the case of a saturated air-water vapour mixture:

• Dry Bulb Temperature (DBT): This is still the actual temperature of the air.
• Wet Bulb Temperature (WBT): When you measure the WBT in saturated air, there is no net evaporation from the wet cloth. Why? Because the air is already holding the maximum possible water vapour. There is no capacity for more water to evaporate into the air. Since there's no evaporation, there is no evaporative cooling effect on the thermometer bulb. Therefore, the wet bulb thermometer reads the same temperature as the dry bulb thermometer.
• Dew Point Temperature (DPT): The dew point is the temperature at which the air becomes saturated upon cooling. In a saturated mixture, the air is *already* saturated at its current temperature. This means if you cool it even slightly below its current temperature, condensation will begin. Thus, the current temperature of the saturated air is its dew point temperature.

Therefore, in a saturated air-water vapour mixture, all three temperatures are equal because there is no further capacity for evaporation (WBT = DBT) and the air is already at the temperature where condensation occurs upon cooling (DPT = DBT).

In a saturated air-water vapour mixture:

DBT = WBT = DPT