Explanation:
The given data is as follows.
Temperature of dry bulb of air = ![25^{o}C](https://tex.z-dn.net/?f=25%5E%7Bo%7DC)
Dew point =
= (10 + 273) K = 283 K
At the dew point temperature, the first drop of water condenses out of air and then,
Partial pressure of water vapor
= vapor pressure of water at a given temperature ![(P^{s}_{a})](https://tex.z-dn.net/?f=%28P%5E%7Bs%7D_%7Ba%7D%29)
Using Antoine's equation we get the following.
![ln (P^{s}_{a}) = 16.26205 - \frac{3799.887}{T(K) - 46.854}](https://tex.z-dn.net/?f=ln%20%28P%5E%7Bs%7D_%7Ba%7D%29%20%3D%2016.26205%20-%20%5Cfrac%7B3799.887%7D%7BT%28K%29%20-%2046.854%7D)
![ln (P^{s}_{a}) = 16.26205 - \frac{3799.887}{283 - 46.854}](https://tex.z-dn.net/?f=ln%20%28P%5E%7Bs%7D_%7Ba%7D%29%20%3D%2016.26205%20-%20%5Cfrac%7B3799.887%7D%7B283%20-%2046.854%7D)
= 0.17079
= 1.18624 kPa
As total pressure
= atmospheric pressure = 760 mm Hg
= 101..325 kPa
The absolute humidity of inlet air = ![\frac{P^{s}_{a}}{P_{t} - P^{s}_{a}} \times \frac{18 kg H_{2}O}{29 \text{kg dry air}}](https://tex.z-dn.net/?f=%5Cfrac%7BP%5E%7Bs%7D_%7Ba%7D%7D%7BP_%7Bt%7D%20-%20P%5E%7Bs%7D_%7Ba%7D%7D%20%5Ctimes%20%5Cfrac%7B18%20kg%20H_%7B2%7DO%7D%7B29%20%5Ctext%7Bkg%20dry%20air%7D%7D%20)
![\frac{1.18624}{101.325 - 1.18624} \times \frac{18 kg H_{2}O}{29 \text{kg dry air}}](https://tex.z-dn.net/?f=%5Cfrac%7B1.18624%7D%7B101.325%20-%201.18624%7D%20%5Ctimes%20%5Cfrac%7B18%20kg%20H_%7B2%7DO%7D%7B29%20%5Ctext%7Bkg%20dry%20air%7D%7D)
= 0.00735 kg
/ kg dry air
Hence, air leaving the humidifier has a has an absolute humidity (%) of 0.07 kg
/ kg dry air.
Therefore, amount of water evaporated for every 1 kg dry air entering the humidifier is as follows.
0.07 kg - 0.00735 kg
= 0.06265 kg
for every 1 kg dry air
Hence, calculate the amount of water evaporated for every 100 kg of dry air as follows.
![0.06265 kg \times 100](https://tex.z-dn.net/?f=0.06265%20kg%20%5Ctimes%20100)
= 6.265 kg
Thus, we can conclude that kg of water the must be evaporated into the air for every 100 kg of dry air entering the unit is 6.265 kg.