Thermodynamics

498 | Thermodynamicsfluid in actual engines contains larger molecules such as carbon dioxide,and the specific heat ratio decreases with temperature, which is one of thereasons that the actual cycles have lower thermal efficiencies than the idealOtto cycle. The thermal efficiencies of actual spark-ignition engines rangefrom about 25 to 30 percent.EXAMPLE 9–2The Ideal Otto CycleP, kPa10032q inIsentropic1v 2 = v 3 = – v8 1Isentropicq outFIGURE 9–19P-v diagram for the Otto cyclediscussed in Example 9–2.41v 1 = v 4vAn ideal Otto cycle has a compression ratio of 8. At the beginning of thecompression process, air is at 100 kPa and 17°C, and 800 kJ/kg of heat istransferred to air during the constant-volume heat-addition process. Accountingfor the variation of specific heats of air with temperature, determine(a) the maximum temperature and pressure that occur during the cycle,(b) the net work output, (c) the thermal efficiency, and (d ) the mean effectivepressure for the cycle.Solution An ideal Otto cycle is considered. The maximum temperature andpressure, the net work output, the thermal efficiency, and the mean effectivepressure are to be determined.Assumptions 1 The air-standard assumptions are applicable. 2 Kinetic andpotential energy changes are negligible. 3 The variation of specific heatswith temperature is to be accounted for.Analysis The P-v diagram of the ideal Otto cycle described is shown inFig. 9–19. We note that the air contained in the cylinder forms a closedsystem.(a) The maximum temperature and pressure in an Otto cycle occur at theend of the constant-volume heat-addition process (state 3). But first we needto determine the temperature and pressure of air at the end of the isentropiccompression process (state 2), using data from Table A–17:Process 1-2 (isentropic compression of an ideal gas):v r2v r1 v 2v 1 1 rT 1 290 K S u 1 206.91 kJ>kgv r1 676.1S v r2 v r1r 676.1 84.51 S T82 652.4 Ku 2 475.11 kJ>kgP 2 v 2T 2 P 1v 1T 1S P 2 P 1 a T 2T 1ba v 1v 2bProcess 2-3 (constant-volume heat addition): 1100 kPa2 a 652.4 K b182 1799.7 kPa290 Kq in u 3 u 2800 kJ>kg u 3 475.11 kJ>kgu 3 1275.11 kJ>kg S T 3 1575.1 Kv r3 6.108