Thermodynamics

344 | ThermodynamicsThe power output of the turbine is determined from the rate form of theenergy balance,E # in E # out dE system /dt 0¡0 (steady)⎫⎪⎪⎬⎪⎪⎭1444444442444444443Rate of net energy transferby heat, work, and massRate of change in internal, kinetic,potential, etc., energiesThe inlet state is completely specified since two properties are given. Butonly one property (pressure) is given at the final state, and we need onemore property to fix it. The second property comes from the observation thatthe process is reversible and adiabatic, and thus isentropic. Therefore, s 2 s 1 , andState 1:State 2:E # in E # outm # h 1 W # out m # h 2 1since Q # 0, ke pe 02W # out m # 1h 1 h 2 2P 1 5 MPaT 1 450°C fh 1 3317.2 kJ>kgs 1 6.8210 kJ>kg # KP 2 1.4 MPafhs 2 s 2 2967.4 kJ>kg1Then the work output of the turbine per unit mass of the steam becomesw out h 1 h 2 3317.2 2967.4 349.8 kJ/kgTINTERACTIVETUTORIALSEE TUTORIAL CH. 7, SEC. 5 ON THE DVD.InternallyreversibleprocessdA = T dS= δQ∫2Area = T dS = Q1FIGURE 7–16On a T-S diagram, the area under theprocess curve represents the heattransfer for internally reversibleprocesses.S7–5 ■ PROPERTY DIAGRAMS INVOLVING ENTROPYProperty diagrams serve as great visual aids in the thermodynamic analysisof processes. We have used P-v and T-v diagrams extensively in previouschapters in conjunction with the first law of thermodynamics. In the secondlawanalysis, it is very helpful to plot the processes on diagrams for whichone of the coordinates is entropy. The two diagrams commonly used in thesecond-law analysis are the temperature-entropy and the enthalpy-entropydiagrams.Consider the defining equation of entropy (Eq. 7–4). It can berearranged asdQ int rev TdS 1kJ2(7–14)As shown in Fig. 7–16, dQ rev int corresponds to a differential area on a T-Sdiagram. The total heat transfer during an internally reversible process isdetermined by integration to be2Q int rev TdS1kJ21(7–15)which corresponds to the area under the process curve on a T-S diagram.Therefore, we conclude that the area under the process curve on a T-S diagramrepresents heat transfer during an internally reversible process. Thisis somewhat analogous to reversible boundary work being represented by