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(III) Air that is at its dew point of 5°C is drawn into a building where it is heated to 22°C. What will be the relative humidity at this temperature? Assume constant pressure of 1.0 atm. Take into account the expansion of the air.

Short Answer

Expert verified

The relative humidity is 32.7%.

Step by step solution

01

Given data

From the given table,

The saturated vapor pressure of water at T1=5C is P1=872Pa.

The saturated vapor pressure of water at T2=20C is P2=2330Pa.

The saturated vapor pressure of water at T3=25C is P3=3170Pa.

Let P4 be the saturated vapor pressure of water at T4=22C.

02

Concepts

The relative humidity is the ratio of the partial pressure of water vapor to the saturated vapor pressure at a given temperature.

Here, you have to use the equationrelativehumidity=P1P4×100%.

03

Calculation

Consider that vapor pressure is increasing linearly between 20C to 25C.

Thus,

cP3P2T3T2=P4P2T4T23170Pa2330Pa25C20C=P42330Pa22C20CP4=2666Pa

Now, the relative humidity at T4=22C is:

cRelativehumidity=P1P4×100%=872Pa2666Pa×100%=32.7%

Hence, the relative humidity is 32.7%.

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