Question

A moist air sample has dry bulb temperature of ${30}^{\circ }C$ and specific humidity of 11.5 g water vapour per kg dry air. Assume molecular weight of air as 28.93. If the saturation vapour pressure of water at ${30}^{\circ }C$ is 4.24 kPa and the total pressure is 90 kPa, then the relative humidity (in %) of air sample is

• A. 50.5
• B. 38.5
• C. 56.5
• D. 68.5

Answer 1

The correct option is B 38.5

Relative humidity,

$\varphi =\frac{p_v}{p_{vs}}$

Specific humidity,

$\omega =0.622\left(\frac{p_v}{p-p_v}\right)$

$11.5\times {10}^{-3}=0.622\left(\frac{p_v}{90-p_v}\right)$

$p_v=1.63378\text{KPa}$

Relative humidity,

$\varphi =\frac{p_v}{p_{vs}}=\frac{1.63378}{4.28}=0.385$

= 38.5%