Question

The air supplied to a room of a building in winter is to be at 17°C and have a relative humidity of 60%. If the barometric pressure is 1.01325 bar, find : 

(i) The specific humidity ; 

(ii) The dew point under these conditions.

Answer 1

Dry bulb temperature, t_db = 17ºC 

Relative humidity, φ = 60% 

Barometric or total pressure, p_t = 1.01325 bar 

Specific humidity, W : 

Corresponding to 17ºC, from steam tables, 

p_vs = 0.0194 bar

φ = \(\cfrac{p_v}{p_{vs}}\)

0.6 = \(\cfrac{p_v}{0.0194}\)

p_v = 0.6 × 0.0194 = 0.01164 bar.

Specific humidity,

W = \(\cfrac{0.622\,p_v}{p_i-p_v}\) = \(\cfrac{0.622\times0.01164}{1.01325-0.01164}\)

= 0.00723 kg/kg of dry air.

Dew point temperature, t_dp : 

If the air is cooled at constant pressure the vapour will begin to condense at the saturation temperature corresponding to 0.01164 bar. By interpolation from steam tables, the dew point temperature, t_dp is then

t_dp = 9 + (10 – 9) × \(\cfrac{0.011642-0.01150}{10.01230-0.01150}\)

= 9.18°C.