Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

Chapter 3 | 139

6 m

5 m

4 m

AIR

P =

T =

m =

100 kPa

25 °C

?

FIGURE 3–48

Schematic for Example 3–10.

EXAMPLE 3–10 Mass of Air in a Room

Determine the mass of the air in a room whose dimensions are 4 m 5 m 

6 m at 100 kPa and 25°C.

Solution The mass of air in a room is to be determined.

Analysis A sketch of the room is given in Fig. 3–48. Air at specified condi-

tions can be treated as an ideal gas. From Table A–1, the gas constant of air

is R
0.287 kPa · m^3 /kg · K, and the absolute temperature is T
25°C 

273 
298 K. The volume of the room is

The mass of air in the room is determined from the ideal-gas relation to be

m

PV

RT

1 100 kPa 21 120 m^32

1 0.287 kPa#m^3 >kg#K 21 298 K 2

140.3 kg

V
 1 4 m 21 5 m 21 6 m 2 
120 m^3

Is Water Vapor an Ideal Gas?

This question cannot be answered with a simple yes or no. The error
involved in treating water vapor as an ideal gas is calculated and plotted in
Fig. 3–49. It is clear from this figure that at pressures below 10 kPa, water
vapor can be treated as an ideal gas, regardless of its temperature, with neg-
ligible error (less than 0.1 percent). At higher pressures, however, the ideal-
gas assumption yields unacceptable errors, particularly in the vicinity of the
critical point and the saturated vapor line (over 100 percent). Therefore, in
air-conditioning applications, the water vapor in the air can be treated as an
ideal gas with essentially no error since the pressure of the water vapor
is very low. In steam power plant applications, however, the pressures
involved are usually very high; therefore, ideal-gas relations should not be
used.

3–7 ■ COMPRESSIBILITY FACTOR—A MEASURE

OF DEVIATION FROM IDEAL-GAS BEHAVIOR

The ideal-gas equation is very simple and thus very convenient to use. How-
ever, as illustrated in Fig. 3–49, gases deviate from ideal-gas behavior sig-
nificantly at states near the saturation region and the critical point. This
deviation from ideal-gas behavior at a given temperature and pressure can
accurately be accounted for by the introduction of a correction factor called
the compressibility factorZdefined as

(3–17)

or

Pv
ZRT (3–18)

Z

Pv

RT

SEE TUTORIAL CH. 3, SEC. 7 ON THE DVD.

INTERACTIVE

TUTORIAL