Thermodynamics, Heat Transfer, And Fluid Flow. V.1. Thermodynamics, страница 13

The energy entering and leaving the system is zero, and you canassume that the ke and pe are constant so that:Q̇ c + Ẇ p = Q̇ sg2)Ẇp= Q̇sgQ̇c= 1.361 x 1010 Btu/hr - 1.36 x 1010 Btu/hr= 1.0 x 107 Btu/hrẆp= 4007 hpOf the examples just completed, emphasis should be placed on the heat exchanger analysis. Boththe primary side and the secondary side have their own energy balances as the heat energy istransferred from one fluid to the other. In calculating heat exchanger heat transfer rates, wefound that we could use the equations Q̇ṁcp∆h .Perhaps a short analysis of the secondary side of the heat exchanger will aid in understandingthe heat exchanger’s importance in the energy conversion process.HT-01Page 66Rev.

0ThermodynamicsFIRST LAW OF THERMODYNAMICSExample 6: Secondary Side of Heat ExchangerSteam flows through a condenser at 2.0 x 106 kg/hr, entering as saturated vapor at 40°C(h = 2574 kj/kg), and leaving at the same pressure as subcooled liquid at 30°C (h = 125.8kJ/kg). Cooling water is available at 18°C (h = 75.6 kJ/kg). Environmental requirementslimit the exit temperature to 25°C (h = 104.9 kJ/kg). Determine the required coolingwater flow rate.Solution:Thermal balance gives the following:Q̇stmQ̇cwṁstm(houtṁcwhin) stmṁcw(houthin) cwṁstm(hout hin) stm/(hout hin) cw= -2.0 x 106 kg/hr (125.8 - 2574 kj/kg)/(104.9 - 75.6 kj/kg)ṁcw1.67 x 108 kg/hrIn this example, we calculated the flow rate using the equation Q̇occurred when the steam was condensed to liquid water.

Q̇ṁ∆h since a phase changeṁcp∆T would not have workedsince ∆T=0 for a phase change. Had we attempted to solve the problem using Q̇ ṁcp∆T , wewould have discovered that an error occurs since the ∆T = 10oC is the ∆T needed to subcool theliquid from saturation at 40oC to a subcooled value of 30oC. Therefore, the heat transfer processto condense the steam to a saturated liquid has not been taken into account.Rev. 0Page 67HT-01FIRST LAW OF THERMODYNAMICSThermodynamicsSummaryThe important information from this chapter is summarized below.First Law of Thermodynamics Summary•The First Law of Thermodynamics states that energy can neither becreated nor destroyed, only altered in form.•In analyzing an open system using the First Law of Thermodynamics, theenergy into the system is equal to the energy leaving the system.•If the fluid passes through various processes and then eventually returnsto the same state it began with, the system is said to have undergone acyclic process.

The first law is used to analyze a cyclic process.•The energy entering any component is equal to the energy leaving thatcomponent at steady state.•The amount of energy transferred across a heat exchanger is dependentupon the temperature of the fluid entering the heat exchanger from bothsides and the flow rates of thse fluids.•A T-s diagram can be used to represent thermodynamic processes.HT-01Page 68Rev. 0ThermodynamicsSECOND LAW OF THERMODYNAMICSSECOND LAW OF THERMODYNAMICSThe Second Law of Thermodynamics is used to determine the maximum efficiencyof any process.

A comparison can then be made between the maximum possibleefficiency and the actual efficiency obtained.EO 1.25STATE the Second Law of Thermodynamics.EO 1.26Using the Second Law of Thermodynamics,DETERMINE the maximum possible efficiency of asystem.EO 1.27Given a thermodynamic system, CONDUCT ananalysis using the Second Law of Thermodynamics.EO 1.28Given a thermodynamic system, DESCRIBE themethod used to determine:a.The maximum efficiency of the systemb.The efficiency of the components within the systemEO 1.29DIFFERENTIATE between the path for an idealprocess and that for a real process on a T-s or h-sdiagram.EO 1.30Given a T-s or h-s diagram for a system EVALUATE:a.System efficienciesb.Component efficienciesEO 1.31DESCRIBE how individual factors affect system orcomponent efficiency.Second Law of ThermodynamicsOne of the earliest statements of the Second Law of Thermodynamics was made by R.

Clausiusin 1850. He stated the following.It is impossible to construct a device that operates in a cycle and produces noeffect other than the removal of heat from a body at one temperature and theabsorption of an equal quantity of heat by a body at a higher temperature.Rev. 0Page 69HT-01SECOND LAW OF THERMODYNAMICSThermodynamicsWith the Second Law of Thermodynamics, the limitations imposed on any process can be studiedto determine the maximum possible efficiencies of such a process and then a comparison can bemade between the maximum possible efficiency and the actual efficiency achieved.

One of theareas of application of the second law is the study of energy-conversion systems. For example,it is not possible to convert all the energy obtained from a nuclear reactor into electrical energy.There must be losses in the conversion process. The second law can be used to derive anexpression for the maximum possible energy conversion efficiency taking those losses intoaccount. Therefore, the second law denies the possibility of completely converting into work allof the heat supplied to a system operating in a cycle, no matter how perfectly designed thesystem may be.

The concept of the second law is best stated using Max Planck’s description:It is impossible to construct an engine that will work in a complete cycle andproduce no other effect except the raising of a weight and the cooling of a heatreservoir.The Second Law of Thermodynamics is needed because the First Law of Thermodynamics doesnot define the energy conversion process completely. The first law is used to relate and toevaluate the various energies involved in a process. However, no information about the directionof the process can be obtained by the application of the first law.

Early in the development ofthe science of thermodynamics, investigators noted that while work could be convertedcompletely into heat, the converse was never true for a cyclic process. Certain natural processeswere also observed always to proceed in a certain direction (e.g., heat transfer occurs from a hotto a cold body). The second law was developed as an explanation of these natural phenomena.EntropyOne consequence of the second law is the development of the physical property of matter termedentropy (S). Entropy was introduced to help explain the Second Law of Thermodynamics. Thechange in this property is used to determine the direction in which a given process will proceed.Entropy can also be explained as a measure of the unavailability of heat to perform work in acycle.

This relates to the second law since the second law predicts that not all heat provided toa cycle can be transformed into an equal amount of work, some heat rejection must take place.The change in entropy is defined as the ratio of heat transferred during a reversible process tothe absolute temperature of the system.HT-01Page 70Rev. 0ThermodynamicsSECOND LAW OF THERMODYNAMICS∆S∆QTabs(For a reversible process)∆S=the change in entropy of a system during some process (Btu/°R)∆Q=the amount of heat added to the system during the process (Btu)Tabs=the absolute temperature at which the heat was transferred (°R)whereThe second law can also be expressed as ∆S≥O for a closed cycle.

In other words, entropy mustincrease or stay the same for a cyclic system; it can never decrease.Entropy is a property of a system. It is an extensive property that, like the total internal energyor total enthalpy, may be calculated from specific entropies based on a unit mass quantity of thesystem, so that S = ms. For pure substances, values of the specific entropy may be tabulatedalong with specific enthalpy, specific volume, and other thermodynamic properties of interest.One place to find this tabulated information is in the steam tables described in a previous chapter(refer back to Figure 19).Specific entropy, because it is a property, is advantageously used as one of the coordinates whenrepresenting a reversible process graphically.

The area under a reversible process curve on theT-s diagram represents the quantity of heat transferred during the process.Thermodynamic problems, processes, and cycles are often investigated by substitution ofreversible processes for the actual irreversible process to aid the student in a second law analysis.This substitution is especially helpful because only reversible processes can be depicted on thediagrams (h-s and T-s, for example) used for the analysis. Actual or irreversible processes cannotbe drawn since they are not a succession of equilibrium conditions. Only the initial and finalconditions of irreversible processes are known; however, some thermodynamics texts representan irreversible process by dotted lines on the diagrams.Rev.

0Page 71HT-01SECOND LAW OF THERMODYNAMICSThermodynamicsCarnot’s PrincipleWith the practice of using reversible processes, Sadi Carnot in 1824 advanced the study of thesecond law by disclosing a principle consisting of the following propositions.1.No engine can be more efficient than a reversible engine operating between thesame high temperature and low temperature reservoirs. Here the term heatreservoir is taken to mean either a heat source or a heat sink.2.The efficiencies of all reversible engines operating between the same constanttemperature reservoirs are the same.3.The efficiency of a reversible engine depends only upon the temperatures of theheat source and heat receiver.Carnot CycleThe above principle is best demonstrated with a simple cycle (shown in Figure 21) and anexample of a proposed heat power cycle.

The cycle consists of the following reversibleprocesses.HT-011-2:adiabatic compression from TC to TH due to work performed on fluid.2-3:isothermal expansion as fluid expands when heat is added to the fluid attemperature TH.3-4:adiabatic expansion as the fluid performs work during the expansion process andtemperature drops from TH to TC.4-1:isothermal compression as the fluid contracts when heat is removed from the fluidat temperature TC.Page 72Rev. 0ThermodynamicsSECOND LAW OF THERMODYNAMICSThis cycle is known as a Carnot Cycle. The heat input (QH) in a Carnot Cycle is graphicallyrepresented on Figure 21 as the area under line 2-3.