Question

The dry bulb temperature (DBT) of atmospheric humid air is \(30^{\circ}\text{C}\). The dew point temperature (DPT) is also \(30^{\circ}\text{C}\) and the humidity ratio is \(0.025\ \dfrac{\text{kg of water vapor}}{\text{kg of dry air}}\).

The relative humidity (RH) of the air is ______ %.

• A. 100
• B. 25
• C. 50
• D. 0

Hint:

Recall that air at its dew point temperature is, by definition, saturated air.

Answer 1

The Correct Option is A

Step 1: Recall what the dew point temperature means.
The dew point temperature of an air vapor mixture is the temperature at which the mixture becomes saturated when cooled at constant pressure, keeping its humidity ratio fixed.

Step 2: Compare DPT with DBT.
Here the dew point temperature (\(30^{\circ}\text{C}\)) equals the dry bulb temperature (\(30^{\circ}\text{C}\)). This means the air is already saturated at its own actual temperature, with no cooling needed.

Step 3: Connect this to relative humidity.
Relative humidity is the ratio of the actual vapor pressure to the saturation vapor pressure at the dry bulb temperature, \(\text{RH} = p_v / p_{sat}(T_{db})\). Since DPT equals DBT, the actual vapor pressure already equals the saturation vapor pressure, so this ratio is exactly 1.

Final Answer:
The stated humidity ratio is only extra information; once DPT equals DBT the air is fully saturated. \[ \boxed{\text{RH} = 100\%} \]