Thermodynamics

496 | ThermodynamicsT21v = const.q inv = const.34q outFIGURE 9–16T-s diagram of the ideal Otto cycle.sMajor car companies have research programs underway on two-strokeengines which are expected to make a comeback in the future.The thermodynamic analysis of the actual four-stroke or two-stroke cyclesdescribed is not a simple task. However, the analysis can be simplified significantlyif the air-standard assumptions are utilized. The resulting cycle,which closely resembles the actual operating conditions, is the ideal Ottocycle. It consists of four internally reversible processes:1-2 Isentropic compression2-3 Constant-volume heat addition3-4 Isentropic expansion4-1 Constant-volume heat rejectionThe execution of the Otto cycle in a piston–cylinder device together witha P-v diagram is illustrated in Fig. 9–13b. The T-s diagram of the Otto cycleis given in Fig. 9–16.The Otto cycle is executed in a closed system, and disregarding thechanges in kinetic and potential energies, the energy balance for any of theprocesses is expressed, on a unit-mass basis, as(9–5)No work is involved during the two heat transfer processes since both takeplace at constant volume. Therefore, heat transfer to and from the workingfluid can be expressed asand(9–6a)(9–6b)Then the thermal efficiency of the ideal Otto cycle under the cold air standardassumptions becomesProcesses 1-2 and 3-4 are isentropic, and v 2 v 3 and v 4 v 1 . Thus,(9–7)Substituting these equations into the thermal efficiency relation and simplifyinggivewhereh th,Otto w netq in1q in q out 2 1w in w out 2 ¢u1kJ>kg2q in u 3 u 2 c v 1T 3 T 2 2q out u 4 u 1 c v 1T 4 T 1 2 1 q out 1 T 4 T 1 1 T 1 1T 4 >T 1 12q in T 3 T 2 T 2 1T 3 >T 2 12T 1 a v k12b a v k13b T 4T 2 v 1 v 4 T 3h th,Otto 1 1r k1(9–8)r V max V 1 v 1(9–9)V min V 2 v 2is the compression ratio and k is the specific heat ratio c p /c v .Equation 9–8 shows that under the cold-air-standard assumptions, thethermal efficiency of an ideal Otto cycle depends on the compression ratioof the engine and the specific heat ratio of the working fluid. The thermalefficiency of the ideal Otto cycle increases with both the compression ratio