Answer: the wet bulb temp is approximately 13.15°c
Explanation: humidity ratio H varies directly with temperature (the hotter the air the more the moisture that vapourises into water vapour increasing the humidity ratio and vice versa)
H1T1 = H2T2
T is the temperatures (dry bulb)
H2 = (4.45 * 30)/20 = 6.675 g/kg
We now have two properties of the second state (temp already given as 20°c) we check psychometric chart for the wet bulb temperature of that state which gives us approximately 13.15°c
