Question

Ambient pressure, temperature, and relative humidity at a location are 101 kPa, 300 K, and 60%, respectively. The saturation pressure of water at 300 K is 3.6 kPa. The specific humidity of ambient air is \(\underline{\hspace{2cm}}\) g/kg of dry air.

• A. 21.4
• B. 35.1
• C. 21.9
• D. 13.6

Hint:

Specific humidity is calculated as the mass of water vapor per unit mass of dry air, and it depends on the partial pressures of water vapor and dry air.

Answer 1

The Correct Option is D

The specific humidity \( \phi \) can be calculated using the formula: \[ \phi = 0.622 \times \frac{p_v}{p_a} \] where:
- \( p_v \) is the partial pressure of water vapor,
- \( p_a \) is the partial pressure of dry air.
We are given:
- Relative humidity \( RH = 60% \),
- Saturation pressure of water \( p_{sat} = 3.6 \, \text{kPa} \),
- \( p_v = RH \times p_{sat} = 0.60 \times 3.6 \, \text{kPa} = 2.16 \, \text{kPa} \),
- Ambient pressure \( p_a = 101 - p_v = 101 - 2.16 = 98.84 \, \text{kPa} \).
The specific humidity is: \[ \phi = 0.622 \times \frac{2.16}{98.84} \times 1000 = 13.6 \, \text{g/kg} \] Thus, the correct answer is (D).