Thermodynamics

Chapter 7 | 377or(b) The actual exit temperature of the air is higher than the isentropic exittemperature evaluated above and is determined fromorV 2s 22 1h 1 h 2s 2 22c p,avg 1T 1 T 2s 2 B2 11.099 kJ>kg # K231950 7482 K4 a1000 m 2 >s 21 kJ>kg b 666 m/sh N h 1 h 2a c p,avg 1T 1 T 2a 2h 1 h 2s c p,avg 1T 1 T 2s 20.92 950 T 2a950 748 S T 2a 764 KThat is, the temperature is 16 K higher at the exit of the actual nozzle as aresult of irreversibilities such as friction. It represents a loss since this rise intemperature comes at the expense of kinetic energy (Fig. 7–56).(c) The actual exit velocity of air can be determined from the definition ofisentropic efficiency of a nozzle,h N V 22aV SV 2 2a 2h N V 2 2s 20.92 1666 m>s2 2 639 m/s2s950 KAIRActual nozzleIsentropic nozzle764 K, 639 m/s748 K, 666 m/sFIGURE 7–56A substance leaves actual nozzles at ahigher temperature (thus a lowervelocity) as a result of friction.7–13 ■ ENTROPY BALANCEThe property entropy is a measure of molecular disorder or randomness ofa system, and the second law of thermodynamics states that entropy canbe created but it cannot be destroyed. Therefore, the entropy change ofa system during a process is greater than the entropy transfer by anamount equal to the entropy generated during the process within the system,and the increase of entropy principle for any system is expressed as(Fig. 7–57)orTotal Total Total Change in the° entropy ¢ ° entropy ¢ ° entropy ¢ ° total entropy ¢entering leaving generated of the systemS in S out S gen ¢S system(7–68)which is a verbal statement of Eq. 7–9. This relation is often referred to asthe entropy balance and is applicable to any system undergoing anyprocess. The entropy balance relation above can be stated as: the entropychange of a system during a process is equal to the net entropy transferthrough the system boundary and the entropy generated within the system.Next we discuss the various terms in that relation.E inS inINTERACTIVETUTORIALSEE TUTORIAL CH. 7, SEC. 13 ON THE DVD.System∆E system∆S systemS gen ≥ 0E outS outgen∆E system = E in – E out∆S system = S in – S out + S genFIGURE 7–57Energy and entropy balances for asystem.