Thermodynamics

490 | ThermodynamicsPT2 33FIGURE 9–5On both P-v and T-s diagrams, thearea enclosed by the process curverepresents the net work of the cycle.1w net4v12w net4sPTT HT L1IsentropicIsentropic4q in1 24q inTH = const.q out2q outIsentropicT L = const.3IsentropicFIGURE 9–6P-v and T-s diagrams of a Carnotcycle.3vsThe T-s diagram is particularly useful as a visual aid in the analysis of idealpower cycles. An ideal power cycle does not involve any internal irreversibilities,and so the only effect that can change the entropy of the workingfluid during a process is heat transfer.On a T-s diagram, a heat-addition process proceeds in the direction ofincreasing entropy, a heat-rejection process proceeds in the direction ofdecreasing entropy, and an isentropic (internally reversible, adiabatic)process proceeds at constant entropy. The area under the process curve on aT-s diagram represents the heat transfer for that process. The area under theheat addition process on a T-s diagram is a geometric measure of the totalheat supplied during the cycle q in , and the area under the heat rejectionprocess is a measure of the total heat rejected q out . The difference betweenthese two (the area enclosed by the cyclic curve) is the net heat transfer,which is also the net work produced during the cycle. Therefore, on a T-sdiagram, the ratio of the area enclosed by the cyclic curve to the area underthe heat-addition process curve represents the thermal efficiency of thecycle. Any modification that increases the ratio of these two areas will alsoincrease the thermal efficiency of the cycle.Although the working fluid in an ideal power cycle operates on a closedloop, the type of individual processes that comprises the cycle depends onthe individual devices used to execute the cycle. In the Rankine cycle, whichis the ideal cycle for steam power plants, the working fluid flows through aseries of steady-flow devices such as the turbine and condenser, whereas inthe Otto cycle, which is the ideal cycle for the spark-ignition automobileengine, the working fluid is alternately expanded and compressed in a piston–cylinder device. Therefore, equations pertaining to steady-flow systemsshould be used in the analysis of the Rankine cycle, and equations pertainingto closed systems should be used in the analysis of the Otto cycle.9–2 ■ THE CARNOT CYCLE AND ITS VALUEIN ENGINEERINGThe Carnot cycle is composed of four totally reversible processes: isothermalheat addition, isentropic expansion, isothermal heat rejection, and isentropiccompression. The P-v and T-s diagrams of a Carnot cycle arereplotted in Fig. 9–6. The Carnot cycle can be executed in a closed system(a piston–cylinder device) or a steady-flow system (utilizing two turbinesand two compressors, as shown in Fig. 9–7), and either a gas or a vapor can