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In winter-time, heated indoor air reduces the relative humidity inside buildings

ID: 3161715 • Letter: I

Question

In winter-time, heated indoor air reduces the
relative humidity inside buildings. This is especially a problem
inside hospitals in cold climates where the air temperature
and relative humidity must be kept at 69ºF (20.6ºC) and 75%
respectively for health and hygiene reasons.

Consider a cold winter day in Chicago when the outside air
temperature is 20ºF (-6.7ºC) and the relative humidity is
90%. (Assume air density is 1.2 kg m-3 and air pressure is
1000 mb).


a) What is the relative humidity inside the hospital building if
the air is brought from outside and heated to the required
temperature, but not humidified?


b) Consider a hospital building with 1500 m3 volume. It has
a humidifier system that vaporizes 1 gallon hr-1 of water
(264.2 gallons = 1 m3). How many hours should the humidifier
be in operation to increase the relative humidity of the indoor
air to the regulation limit?

Explanation / Answer

outside air

RH = 0.9   temp = -6.7 C

vapor pressure = 0.9SVP(-6.7)

RH at 20.6 C = 0.9SVP(-6.7)/SVP(20.6) = 0.9*0.61/2.34 = 0.23

    = 23%

volume of the building = 1500 m3

RH = 0.75 required

vapor pressure required at 20.6 C  

density of air = 1.2 kg /m3

saturation vapor density at 20.6 C   = 17.3 gm/m3

amount of water vapor required = 0.75*17.3 = 12.96 g/m3

amount of water vapor available   = 0.23*17.3 = 3.98 g/m3

amount of watre vapor to be added = 12.96 - 3.98 =9.0 g/m3

Total amount of water vapor to be added for the whole building = 0.9*1500 = 1350 gm

volume of water = 1.35e-3 m3     = 0.357 gallons

The humidifier vaporises 1 gallong per hr

The humidifier need to be run for 21.42 mts

It has to be operated for 245 hrs.