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

The correct option is: P_𝑣 = 0.622 P_{����𝑎t}.

Step-by-Step Explanation:

In psychrometrics and thermodynamics, an air-water vapour mixture is often analyzed using the molecular weights of the constituent gases. The ratio of the molecular mass of water vapour (M_w ≈ 18.016 g/mol) to the molecular mass of dry air (M_a ≈ 28.97 g/mol) is a fundamental constant used in calculations.

This molecular weight ratio is given by:

$$\frac{M_w}{M_a}=\frac{18.016}{28.97}\approx 0.622$$

This constant of 0.622 is key in defining relations such as specific humidity (humidity ratio). For the given air-water mixture, this ratio establishes the correct proportional relation between the partial pressure of water vapour P_v and the saturation pressure P_sat as:

$$P_v=0.622P_{\mathrm{sat}}$$