Thermodynamics

the area under the process curve on a P-V diagram. Note that the area underthe process curve represents heat transfer for processes that are internally(or totally) reversible. The area has no meaning for irreversible processes.Equations 7–14 and 7–15 can also be expressed on a unit-mass basis asand(7–16)(7–17)To perform the integrations in Eqs. 7–15 and 7–17, one needs to know therelationship between T and s during a process. One special case for whichthese integrations can be performed easily is the internally reversibleisothermal process. It yieldsordq int rev Tds1kJ>kg22q int rev Tds1kJ>kg21Q int rev T 0 ¢S1kJ2q int rev T 0 ¢s1kJ>kg2(7–18)(7–19)where T 0 is the constant temperature and S is the entropy change of thesystem during the process.An isentropic process on a T-s diagram is easily recognized as a verticallinesegment. This is expected since an isentropic process involves noheat transfer, and therefore the area under the process path must be zero(Fig. 7–17). The T-s diagrams serve as valuable tools for visualizing thesecond-law aspects of processes and cycles, and thus they are frequentlyused in thermodynamics. The T-s diagram of water is given in the appendixin Fig. A–9.Another diagram commonly used in engineering is the enthalpy-entropydiagram, which is quite valuable in the analysis of steady-flow devices suchas turbines, compressors, and nozzles. The coordinates of an h-s diagramrepresent two properties of major interest: enthalpy, which is a primaryproperty in the first-law analysis of the steady-flow devices, and entropy,which is the property that accounts for irreversibilities during adiabaticprocesses. In analyzing the steady flow of steam through an adiabatic turbine,for example, the vertical distance between the inlet and the exit statesh is a measure of the work output of the turbine, and the horizontal distances is a measure of the irreversibilities associated with the process(Fig. 7–18).The h-s diagram is also called a Mollier diagram after the German scientistR. Mollier (1863–1935). An h-s diagram is given in the appendix forsteam in Fig. A–10.TChapter 7 | 34512s 2 = s 1IsentropicprocessFIGURE 7–17The isentropic process appears as avertical line segment on a T-s diagram.h1∆s2∆hFIGURE 7–18For adiabatic steady-flow devices, thevertical distance h on an h-s diagramis a measure of work, and thehorizontal distance s is a measure ofirreversibilities.ssEXAMPLE 7–6The T-S Diagram of the Carnot CycleShow the Carnot cycle on a T-S diagram and indicate the areas that representthe heat supplied Q H , heat rejected Q L , and the net work output W net,outon this diagram.