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 _______ g/kg of dry air.
1. 35.1
2. 21.9
3. 13.6
4. 21.4

Answer 1

Correct Answer - Option 3 : 13.6

Concept:

Let ‘P’ be the atmospheric pressure in (kPa)

‘ϕ’ be the relative humidity, ‘Pv’ be the partial pressure of the air in (kPa), ‘Pvs’ be the saturation pressure of water in (kPa), ‘ω’ be the specific humidity of air in (kg/kg of dry air).

\(ϕ = \frac{{{P_v}}}{{{P_{vs}}}} \)

\(ω = 0.622\;\times\frac{{{P_v}}}{{\left( {P\ - \ {P_v}} \right)}} \)

Given:

Calculation:

P = 101 kPa, ϕ = 0.6, P_vs = 3.6 kPa

\(ϕ = \frac{{{P_{v}}}}{{{P_{vs}}}} \Rightarrow 0.6 = \frac{{P_v}}{{{3.6}}}\)

P_v = 2.16 kPa

\(ω = 0.622 \times\frac{{{P_v}}}{{\left( {P\ - \ {P_v}} \right)}} \)

\(\omega = 0.622\times\frac{{2.16}}{{\left( {101 \ - \ 2.16} \right)}} \)

∴ ω =  0.0135928 kg of water vapor/kg of dry air.

∴ ω = 13.59 gm of water vapor/kg of dry air.