Heating Ventilating and Air Conditioning: Analysis and Design
6th Edition
ISBN: 9780471470151
Author: Faye C. McQuiston, Jeffrey D. Spitler, Jerald D. Parker
Publisher: Wiley, John & Sons, Incorporated

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Textbook Question
Chapter 3, Problem 3.1P

A space is at a temperature of 75 F (24 C), and the relative humidity is 45 percent. Find (a) the partial pressures of the air and water vapor, (b) the vapor density, and (c) the humidity ratio of the mixture. Assume standard sea-level pressure.

(a)

Expert Solution
To determine

The partial pressure of the air.

The partial pressure of water vapor.

The value of partial pressure of air is 99.57kPa .

The value of partial pressure of vapor is 1.43kPa .

Explanation of Solution

Given:

The temperature of the space is T=75F(24°C) .

The relative humidity is ϕr=45% .

Formula used:

The expression for the partial pressure of air is given as,

Pa=PatmPv

Here, Patm is the atmospheric pressure and its value is 101kPa and Pv is the vapor pressure.

The expression for the partial pressure of vapor is given as,

Pv=ϕrPs

Here, Ps is the saturation temperature at 24°C .

Calculation:

The partial pressure of vapor can be calculated as,

Pv=ϕrPsPv=0.45×(3.17kPa)Pv=1.43kPa

The partial pressure of air can be calculated as,

Pa=PatmPvPa=(1011.43)kPaPa=99.57kPa

Conclusion:

Therefore, the value of partial pressure of air is 99.57kPa .

Therefore, the value of partial pressure of vapor is 1.43kPa .

(b)

Expert Solution
To determine

The vapor density.

The value of vapor density is 0.0104kg/m3 .

Explanation of Solution

Given:

The temperature of the space is T=75F(24°C) .

The relative humidity is ϕr=45% .

Formula used:

The expression for the vapor density is given as,

ρv=PvRv×T

Here, Rv is the gas constant of water vapor and its value is 462.5J/kgK .

Calculation:

The vapor density can be calculated as,

ρv=PvRv×Tρv=1430Pa462.5J/kgK×( 297K)ρv=0.0104kg/m3

Conclusion:

Therefore, the value of vapor density is 0.0104kg/m3 .

(c)

Expert Solution
To determine

The humidity ratio of the mixture.

The value of humidity ratio is 0.00893kgv/kga .

Explanation of Solution

Given:

The temperature of the space is T=75F(24°C) .

The relative humidity is ϕr=45% .

Formula used:

The expression for the humidity ratio is given as,

W=0.6219×Pv(Pa+Pv)Pv

Calculation:

The humidity ratio can be calculated as,

W=0.6219×Pv( P a + P v )PvW=0.6219×1.43kPa( 99.57+1.43)kPa1.43kPaW=0.00893kgv/kga

Conclusion:

Therefore, the value of humidity ratio is 0.00893kgv/kga .

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