Humidity from Wet and Dry Bulb Temperatures. An air–water vapor mixture has a dry bulb temperature of 65.6°C and a wet bulb temperature of 32.2°C. What is the humidity of the mixture?
The correct answer and explanation is :
To find the humidity of an air–water vapor mixture given the dry bulb and wet bulb temperatures, we need to determine the relative humidity (RH). The dry bulb temperature (DBT) is the actual air temperature, and the wet bulb temperature (WBT) reflects the lowest temperature air can reach through evaporative cooling. The larger the difference between DBT and WBT, the drier the air is.
Given:
- Dry Bulb Temperature (T_dry) = 65.6°C
- Wet Bulb Temperature (T_wet) = 32.2°C
Step 1: Use an online psychrometric calculator or chart (or derive using equations), but for simplicity and precision at this high temperature range, we use a psychrometric equation:
The formula for Relative Humidity (RH) (approximation method) is:
[
RH = 100 \times \frac{e_w – \gamma \cdot (T_{dry} – T_{wet})}{e_s}
]
Where:
- ( e_s ) = saturation vapor pressure at dry bulb temp
- ( e_w ) = saturation vapor pressure at wet bulb temp
- ( \gamma ) = psychrometric constant ≈ 0.00066 × pressure (assuming atmospheric pressure of 101.325 kPa)
- ( T_{dry}, T_{wet} ) in °C
Step 2: Use saturated vapor pressure (from steam tables or Antoine equation):
- At 65.6°C → ( e_s \approx 25.05 ) kPa
- At 32.2°C → ( e_w \approx 4.79 ) kPa
Assume standard pressure: ( \gamma = 0.00066 \times 101.325 \approx 0.0669 )
Step 3: Plug into the formula:
[
RH = 100 \times \frac{4.79 – 0.0669 \cdot (65.6 – 32.2)}{25.05}
]
[
RH = 100 \times \frac{4.79 – 0.0669 \cdot 33.4}{25.05}
]
[
RH = 100 \times \frac{4.79 – 2.23446}{25.05} = 100 \times \frac{2.55554}{25.05}
]
[
RH \approx 10.2\%
]
✅ Final Answer:
Relative Humidity ≈ 10.2%
📘 Explanation:
Humidity measures how much water vapor is in the air compared to how much it could hold at that temperature. The dry bulb temperature represents the air’s thermal content, while the wet bulb includes cooling from evaporation. The bigger the gap between the two, the lower the moisture in the air.
In this case, the dry bulb is very high (65.6°C) and the wet bulb is significantly lower (32.2°C), indicating very dry air. The computed relative humidity of 10.2% confirms that this air mixture is extremely dry—common in hot industrial settings or deserts.
This calculation is important in HVAC, meteorology, and thermal comfort applications.