Question

The relative humidity of ambient air at 300 K is 50% with a partial pressure of water vapour equal to P_v. The saturation pressure of water at 300 K is P_sat. The correct relation for the air-water mixture is 
1. P_v = 2P_sat
2. P_v = P_sat
3. P_v = 0.5P_sat
4. P_v = 0.622P_sat

Answer 1

Correct Answer - Option 3 : P_v = 0.5P_sat

Concept:

Relative humidity (ϕ):

If is defined as the ratio of the mass of vapour when air is not saturator to the mass of vapour when air is saturated. It represents the water vapour absorbing capacity.

\(\phi = \frac{{{m_v}}}{{{m_{vs}}}}\)

Also,

\(\frac{{{m_v}}}{{{m_{vs}}}} = \frac{{{P_v}}}{{{P_{vs}}}}\)

Therefore, \(\phi = \frac{{{P_v}}}{{{P_{vs}}}}\)

Where, P_v = Partial pressure of vapour when air is not saturated; P_vs = Partial pressure of vapour, when air is saturated(P_sat).

Calculation:

Given:

ϕ = 0.5,

\(\phi = \frac{{{P_v}}}{{{P_{vs}}}}\)

∴ P_v = 0.5 P_vs

Or

Pv = 0.5 Psat