Thermodynamics

and adiabatic (Fig. 7–14). A process during which the entropy remains During an internally reversible,constant is called an isentropic process. It is characterized byadiabatic (isentropic) process, theIsentropic process: ¢s 0ors 2 s 1 1kJ>kg # K2 (7–13) Chapter 7 | 343SteamTherefore, the entropy change of water during this process iss1¢S m 1s 2 s 1 2 13 lbm2 11.7761 0.074592 Btu>lbm # R 5.105 Btu/RNo irreversibilities(internally reversible)7–4 ISENTROPIC PROCESSES■ No heat transferWe mentioned earlier that the entropy of a fixed mass can be changed by(1) heat transfer and (2) irreversibilities. Then it follows that the entropy ofa fixed mass does not change during a process that is internally reversible(adiabatic)FIGURE 7–14s 2 = s 1That is, a substance will have the same entropy value at the end of theprocess as it does at the beginning if the process is carried out in an isentropicmanner.Many engineering systems or devices such as pumps, turbines, nozzles,and diffusers are essentially adiabatic in their operation, and they performbest when the irreversibilities, such as the friction associated with theprocess, are minimized. Therefore, an isentropic process can serve as anappropriate model for actual processes. Also, isentropic processes enable usto define efficiencies for processes to compare the actual performance ofthese devices to the performance under idealized conditions.It should be recognized that a reversible adiabatic process is necessarilyisentropic (s 2 s 1 ), but an isentropic process is not necessarily a reversibleadiabatic process. (The entropy increase of a substance during a process asa result of irreversibilities may be offset by a decrease in entropy as a resultof heat losses, for example.) However, the term isentropic process is customarilyused in thermodynamics to imply an internally reversible, adiabaticprocess.T1.4 MPaINTERACTIVETUTORIALSEE TUTORIAL CH. 7, SEC. 4 ON THE DVD.5 MPa12Isentropicexpansions 2 = s 1sEXAMPLE 7–5Isentropic Expansion of Steam in a TurbineSteam enters an adiabatic turbine at 5 MPa and 450°C and leaves at a pressureof 1.4 MPa. Determine the work output of the turbine per unit mass ofsteam if the process is reversible.Solution Steam is expanded in an adiabatic turbine to a specified pressurein a reversible manner. The work output of the turbine is to be determined.Assumptions 1 This is a steady-flow process since there is no change withtime at any point and thus m CV 0, E CV 0, and S CV 0. 2 Theprocess is reversible. 3 Kinetic and potential energies are negligible. 4 Theturbine is adiabatic and thus there is no heat transfer.Analysis We take the turbine as the system (Fig. 7–15). This is a controlvolume since mass crosses the system boundary during the process. We notethat there is only one inlet and one exit, and thus ṁ 1 ṁ 2 ṁ.P 1 5 MPaT 1 450CSTEAMTURBINEP 2 1.4 MPas 2 s 1w out ?FIGURE 7–15Schematic and T-s diagram forExample 7–5.