Thermodynamics

360 | ThermodynamicsThe quantity T/P r is a function of temperature only and is defined as relativespecific volume v r . Thus,a v 2b v r2v 1 sconst. v r1(7–50)Equations 7–49 and 7–50 are strictly valid for isentropic processes ofideal gases only. They account for the variation of specific heats with temperatureand therefore give more accurate results than Eqs. 7–42 through7–47. The values of P r and v r are listed for air in Table A–17.EXAMPLE 7–10Isentropic Compression of Air in a Car EngineAir is compressed in a car engine from 22°C and 95 kPa in a reversible andadiabatic manner. If the compression ratio V 1 /V 2 of this engine is 8, determinethe final temperature of the air.Solution Air is compressed in a car engine isentropically. For a given compressionratio, the final air temperature is to be determined.Assumptions At specified conditions, air can be treated as an ideal gas.Therefore, the isentropic relations for ideal gases are applicable.Analysis A sketch of the system and the T-s diagram for the process aregiven in Fig. 7–38.This process is easily recognized as being isentropic since it is bothreversible and adiabatic. The final temperature for this isentropic processcan be determined from Eq. 7–50 with the help of relative specific volumedata (Table A–17), as illustrated in Fig. 7–39.For closed systems:At T 1 295 K:V 2V 1 v 2v 1v r1 647.9From Eq. 7–50:v r2 v r1 a v 2v 1b 1647.92a 1 8 b 80.99 S T 2 662.7 KTherefore, the temperature of air will increase by 367.7°C during thisprocess.FIGURE 7–38Schematic and T-s diagram forExample 7–10.AIRP 1 = 95 kPaT 1 = 295 KV 1= 8V 2T, K29521v 2 = const.Isentropiccompressionv 1 = const.s