Thermodynamics

cen84959_ch03.qxd 4/25/05 2:47 PM Page 139EXAMPLE 3–10Mass of Air in a RoomChapter 3 | 1396 mDetermine 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 conditionscan be treated as an ideal gas. From Table A–1, the gas constant of airis R 0.287 kPa · m 3 /kg · K, and the absolute temperature is T 25°C 273 298 K. The volume of the room isV 14 m215 m2 16 m2 120 m 3The mass of air in the room is determined from the ideal-gas relation to bem PVRT 1100 kPa2 1120 m 3 210.287 kPa # m 3 >kg # K21298 K2 140.3 kg4 mAIRP = 100 kPaT = 25°Cm = ?FIGURE 3–48Schematic for Example 3–10.5 mIs Water Vapor an Ideal Gas?This question cannot be answered with a simple yes or no. The errorinvolved in treating water vapor as an ideal gas is calculated and plotted inFig. 3–49. It is clear from this figure that at pressures below 10 kPa, watervapor can be treated as an ideal gas, regardless of its temperature, with negligibleerror (less than 0.1 percent). At higher pressures, however, the idealgasassumption yields unacceptable errors, particularly in the vicinity of thecritical point and the saturated vapor line (over 100 percent). Therefore, inair-conditioning applications, the water vapor in the air can be treated as anideal gas with essentially no error since the pressure of the water vaporis very low. In steam power plant applications, however, the pressuresinvolved are usually very high; therefore, ideal-gas relations should not beused.3–7 ■ COMPRESSIBILITY FACTOR—A MEASUREOF DEVIATION FROM IDEAL-GAS BEHAVIORThe ideal-gas equation is very simple and thus very convenient to use. However,as illustrated in Fig. 3–49, gases deviate from ideal-gas behavior significantlyat states near the saturation region and the critical point. Thisdeviation from ideal-gas behavior at a given temperature and pressure canaccurately be accounted for by the introduction of a correction factor calledthe compressibility factor Z defined asINTERACTIVETUTORIALSEE TUTORIAL CH. 3, SEC. 7 ON THE DVD.orZ PvRTPv ZRT(3–17)(3–18)