Thermodynamics

492 | ThermodynamicsTT Hq1 in2T L4 3q outs 1 = s 4 s 2 = s 3FIGURE 9–8T-s diagram for Example 9–1.sAnalysis The T-s diagram of a Carnot cycle is redrawn in Fig. 9–8. All fourprocesses that comprise the Carnot cycle are reversible, and thus the areaunder each process curve represents the heat transfer for that process. Heatis transferred to the system during process 1-2 and rejected during process3-4. Therefore, the amount of heat input and heat output for the cycle canbe expressed asq in T H 1s 2 s 1 2andq out T L 1s 3 s 4 2 T L 1s 2 s 1 2since processes 2-3 and 4-1 are isentropic, and thus s 2 s 3 and s 4 s 1 .Substituting these into Eq. 9–1, we see that the thermal efficiency of aCarnot cycle ish th w netq in 1 q outq in 1 T L 1s 2 s 1 2T H 1s 2 s 1 2 1 T LT HDiscussion Notice that the thermal efficiency of a Carnot cycle is independentof the type of the working fluid used (an ideal gas, steam, etc.) orwhether the cycle is executed in a closed or steady-flow system.AIRFUELAIRCombustionchamber(a) ActualHEATHeatingsection(b) IdealCOMBUSTIONPRODUCTSAIRFIGURE 9–9The combustion process is replaced bya heat-addition process in ideal cycles.9–3 ■ AIR-STANDARD ASSUMPTIONSIn gas power cycles, the working fluid remains a gas throughout the entirecycle. Spark-ignition engines, diesel engines, and conventional gas turbinesare familiar examples of devices that operate on gas cycles. In all theseengines, energy is provided by burning a fuel within the system boundaries.That is, they are internal combustion engines. Because of this combustionprocess, the composition of the working fluid changes from air and fuel tocombustion products during the course of the cycle. However, consideringthat air is predominantly nitrogen that undergoes hardly any chemical reactionsin the combustion chamber, the working fluid closely resembles air atall times.Even though internal combustion engines operate on a mechanical cycle(the piston returns to its starting position at the end of each revolution), theworking fluid does not undergo a complete thermodynamic cycle. It isthrown out of the engine at some point in the cycle (as exhaust gases)instead of being returned to the initial state. Working on an open cycle is thecharacteristic of all internal combustion engines.The actual gas power cycles are rather complex. To reduce the analysis toa manageable level, we utilize the following approximations, commonlyknown as the air-standard assumptions:1. The working fluid is air, which continuously circulates in a closed loopand always behaves as an ideal gas.2. All the processes that make up the cycle are internally reversible.3. The combustion process is replaced by a heat-addition process from anexternal source (Fig. 9–9).4. The exhaust process is replaced by a heat-rejection process that restoresthe working fluid to its initial state.Another assumption that is often utilized to simplify the analysis evenmore is that air has constant specific heats whose values are determined at