Thermodynamics

Isothermalcompressorq out43IsentropiccompressorChapter 9 | 4911IsothermalIsentropicturbineturbine w netq inFIGURE 9–72A steady-flow Carnot engine.h th,Carnot 1 T L(9–2)T Hbe utilized as the working fluid. The Carnot cycle is the most efficient cyclethat can be executed between a heat source at temperature T H and a sink attemperature T L , and its thermal efficiency is expressed asReversible isothermal heat transfer is very difficult to achieve in realitybecause it would require very large heat exchangers and it would take a verylong time (a power cycle in a typical engine is completed in a fraction of asecond). Therefore, it is not practical to build an engine that would operateon a cycle that closely approximates the Carnot cycle.The real value of the Carnot cycle comes from its being a standardagainst which the actual or the ideal cycles can be compared. The thermalefficiency of the Carnot cycle is a function of the sink and source temperaturesonly, and the thermal efficiency relation for the Carnot cycle(Eq. 9–2) conveys an important message that is equally applicable to bothideal and actual cycles: Thermal efficiency increases with an increasein the average temperature at which heat is supplied to the system or witha decrease in the average temperature at which heat is rejected fromthe system.The source and sink temperatures that can be used in practice are notwithout limits, however. The highest temperature in the cycle is limited bythe maximum temperature that the components of the heat engine, such asthe piston or the turbine blades, can withstand. The lowest temperature islimited by the temperature of the cooling medium utilized in the cycle suchas a lake, a river, or the atmospheric air.EXAMPLE 9–1Derivation of the Efficiency of the Carnot CycleShow that the thermal efficiency of a Carnot cycle operating between thetemperature limits of T H and T L is solely a function of these two temperaturesand is given by Eq. 9–2.Solution It is to be shown that the efficiency of a Carnot cycle depends onthe source and sink temperatures alone.