Technology & Engineering
Carnot Vapor Cycle
The Carnot vapor cycle is a theoretical thermodynamic cycle that represents the most efficient process for converting heat into work. It consists of four reversible processes: isentropic compression, constant pressure heat addition, isentropic expansion, and constant pressure heat rejection. While it is an idealized model and not practically achievable, it serves as a benchmark for the maximum efficiency of real-world heat engines.
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10 Key excerpts on "Carnot Vapor Cycle"
eBook - PDF- Kaufui Vincent Wong(Author)
- 2011(Publication Date)
- CRC Press(Publisher)
6 -1 6 Vapor Power Systems 6.1 The Carnot Vapor Cycle The.Carnot.cycle.is.the.most.efficient.cycle.operating.between.two.specified.temperature. levels. .The.Carnot.cycle.operating.within.the.two-phase.region.of.a.pure.substance.is.shown. in.Figure.6 .1. .The.working.fluid.is.heated.reversibly.and.isothermally.in.a.boiler.(process. 1-2),.expanded.isentropically.in.a.turbine.(process.2-3),.condensed.reversibly.and.isother-mally.in.a.condenser.(process.3-4),.and.compressed.isentropically.by.a.compressor.to.the. initial.state.(process.4-1) . .The.Carnot.cycle.is.represented.by.a.rectangle.on.a.T-s.diagram . There.are.some.impracticalities.in.the.cycle.as.described: . 1 . . Operating.the.cycle.within.the.saturation.dome.of.a.pure.substance.severely.limits. the.maximum.temperature.that.can.be.used.in.the.cycle . .This.limits.the.maxi-mum.temperature.in.the.cycle,.which.thus.limits.the.thermal.efficiency . .Raising. the.maximum.temperature.in.the.cycle.will.require.heat.transfer.to.the.working. fluid.in.a.single.phase,.which.is.not.easily.done.isothermally . . 2 . . The.isentropic.expansion.can.be.approached.practically.by.a.well-designed.tur-bine. . However,. the. turbine. will. have. to. handle. steam. with. low. quality,. that. is,. steam.containing.a.large.portion.of.moisture . .The.impingement.of.liquid.droplets. on.the.turbine.blades.causes.erosion.and.the.turbine.blades.cannot.last.very.long. under.such.conditions . .Steam.with.less.than.90%.quality.is.not.used.practically.in. steam.turbines . . 3 . . The.isentropic.compression.process.in.the.pump.causes.two.problems . .It.is.dif-ficult.to.control.the.condensation.process.so.as.to.end.up.with.the.desired.quality. at.state.4 . .It.is.not.practical.to.engineer.a.compressor.that.will.handle.two.phases . 6.2 Rankine Cycle: Ideal Cycle for Vapor Power Cycles The.impracticalities.of.the.Carnot.cycle.can.be.eliminated.by.superheating.the.steam.in. the.boiler.and.completely.liquefying.it.in.the.condenser .
eBook - ePub- Nihal E Wijeysundera(Author)
- 2016(Publication Date)
- WSPC(Publisher)
Chapter 9
Vapor Power Cycles
In this chapter we shall consider the analysis of vapor power cycles that convert the stored energy of fuels to mechanical work. The main distinguishing feature of these power cycles is that the working fluid undergoes phase change during the operation of the cycle. Steam power plants, which use water as the working fluid, generate much of the electrical power in the world. Although the design and construction of such power plants involve many engineering considerations, our focus in this chapter will be the thermodynamic aspects that impact on the efficiency of the plant.9.1The Carnot Cycle Using a Vapor
In chapter 6 we discussed the operation of the Carnot heat engine cycle and derived an expression for its efficiency when the working fluid is an ideal gas. The feasibility of operating a Carnot cycle using a vapor is considered in this section. Figure 9.1 shows the T-s diagram of a Carnot cycle in which all processes occur within the liquid-vapor region. The working fluid enters the evaporator at 4 as a saturated liquid where it is heated to a saturated vapor state and exits at 1. The vapor undergoes an isentropic expansion 1-2 to produce a work output. During the condensation process 2-3 the wet vapor rejects heat to a heat sink at constant temperature. Finally, the vapor is compressed from 3 to 4 in an isentropic compression process to complete the cycle.We now apply the SFEE to each of the steady-flow processes of the cycle, neglecting the kinetic and potential energy of the fluid, to obtain the following expressions. Fig. 9.1 Carnot cycle using a vapor For the process 4-1 in the evaporator:where is the steady mass flow rate of the working fluid.For the heat removal process 2-3: Applying the first law to the cycle, the net work output is The efficiency of the cycle 1-2-3-4 is given byManipulating Eqs. (9.1) to (9.4) we haveWe relate the enthalpy changes in Eq. (9.5)
eBook - PDF- S. C. McBirnie(Author)
- 2013(Publication Date)
- Butterworth-Heinemann(Publisher)
354 9 S T E A M -E N G I N E A N D T U R B I N E C Y C L E S A N D E F F I C I E N C I E S 3 5 5 This chapter is concerned only with the cycle efficiency, i.e., the maximum efficiency which can be attained with any given steam conditions and any given cycle operations, inde-pendent of the type of engine or of its losses. Carnot's principle In 1824 the French physicist Nicholas J o s e p h Sadi-Carnot laid down the fundamental requirements of a heat-engine cycle of maximum efficiency in a short statement called Carnot's Principle. No heat engine can be more efficient than one which is completely reversible within itself when working between the same temperature limits. This statement is quite general—it does not say that we must use a steam engine, or a steam turbine, or a oil engine, or a gas turbine; it merely states that if we wish to aim at maximum efficiency, then there are only two qualifications: (i) Reversibility;* (ii) Temperature limits. Bearing in mind the two laws of thermodynamics and the qualifications for reversibility, let us examine the implications of Carnot's Principle. In all heat-engine cycles it is necessary to add heat to the working substance at some point in the cycle. To be revers-ible, such heat reception must be at constant temperature (see page 349). Similarly, it is necessary to take heat from the working substance at some point in the cycle, and this heat rejection is reversible only if it takes place at constant tem-perature. Thus, to comply with Carnot's Principle, all heat received must be received at constant temperature, and all heat rejected must be rejected at constant temperature. Carnot's Principle also states when working between the same temperature limits. This means that for maximum efficiency the upper temperature limit should be as high as possible and the lower temperature limit as low as possible.
No longer available |Learn more- Irving Granet, Maurice Bluestein(Authors)
- 2014(Publication Date)
- CRC Press(Publisher)
Figure 8.1b shows the Carnot gas cycle plotted on pV coordinates. All the conclusions pertain-ing to the efficiency of the vapor cycle also pertain to the gas cycle, because we have already noted that the efficiency of a Carnot cycle is independent of the working fluid in the cycle. Unfortunately, there are certain practical limitations on the upper and lower tempera-tures. The upper temperature is limited by the strength of available materials and the lower by ambient conditions. Recent advances in the field of thermonuclear reactions have indicated that the upper temperature limitation may be removed by using magnetic fields to contain the working fluid. To date, the limits on the upper temperature of power cycles have depended on advances in the field of metallurgy. 8.3 The Rankine Cycle The Carnot cycle described in Section 8.2 cannot be used in a practical device for many reasons. Fluid expansion ( C to D ) would require the handling of relatively wet steam, which is detrimental to modern equipment such as turbines. Further, fluid compression T p s V B B C A D Q in Q r A A ´ C D D ´ T 1 T 2 T 2 T 1 Saturated liquid Saturated vapor Q r = T 2 s = constant = constant (a) (b) FIGURE 8.1 Carnot cycle. (a) Vapor cycle. (b) Gas cycle. 376 Thermodynamics and Heat Power ( A to B ) would also involve wet steam, which requires more work than that needed to com-press a liquid. Thus, point C should be stretched out into the superheat region so expan-sion involves only the gas phase, and point A should be extended to the saturated liquid point so compression involves only a liquid. Historically, the prototype of actual vapor cycles was the simple Rankine cycle. The elements of this cycle are shown in Figure 8.2; the T – s and h – s diagrams for the ideal Rankine cycle are illustrated in Figure 8.3. As indicated in the schematic of Figure 8.2, this cycle consists of four distinct processes.
eBook - PDFThermodynamics
From Concepts to Applications, Second Edition
- Arthur Shavit, Chaim Gutfinger(Authors)
- 2008(Publication Date)
- CRC Press(Publisher)
2 3 Boiler Turbine Pump Condenser 4 1 FIGURE 11.2 Vapor cycle engine. 3 4 1 2 T s FIGURE 11.1 Carnot cycle. There are, however, some practical difficulties associated with the vapor Carnot cycle. The pumping process 1–2 is problematic, as at the inlet to the pump the fluid is composed of two phases, liquid and vapor. Pumps do not operate well under these conditions. The expansion process 3–4 has also complications, since during the expansion a liquid phase in the form of droplets is created. These droplets, which move at high speed, may cause accelerated erosion of the turbine blades. 272 Thermodynamics: From Concepts to Applications Cycles that overcome the difficulties of the Carnot cycle have been devised and are being used in practice. In this chapter we describe the more important of these cycles. In each case, we first present the basic concept of the ideal cycle. We then discuss some of the practical limitations of the cycle, and show how the major parameters are calculated. We start with vapor cycles, that is, cycles in which the working fluid undergoes a liquid– vapor phase change. We then proceed with gas cycles, where the working fluid can be approximated by an ideal gas, including cycles for internal combustion engines. Finally refrigeration cycles are described. 11.1 Rankine Cycle The Rankine* cycle is a practical modification of the Carnot Vapor Cycle. Several configura-tions are classified under the general heading of Rankine cycles; we shall discuss the more important ones. The basic Rankine cycle, shown on a T – s diagram in Figure 11.3, consists essentially of the same elements as the Carnot Vapor Cycle of Figure 11.2. All the processes in the basic Rankine cycle are internally reversible. Saturated liquid, point 1, is pumped into the boiler, point 2, where it is heated at constant pressure to a super-heated steam at point 3.
- Allan D. Kraus, James R. Welty, Abdul Aziz(Authors)
- 2011(Publication Date)
- CRC Press(Publisher)
The Second Law of Thermodynamics 163 Q H T H Q L T L P V 1 2 3 4 FIGURE 6.16 The P -V diagram for the reversed Carnot cycle showing four reversible processes. Then, after substitution of Equation 6.17 into Equation 6.13, the efficiency of the Carnot cycle is seen to be C = 1 − T L T H (6.18) Even though this efficiency has been derived for an ideal gas, it applies to every reversible engine operating between the temperature limits of T H and T L . When we compare Equations 6.2 and 6.18, we find that for a Carnot cycle and indeed for any reversible cycle that Q L Q H = T L T H (6.19) Equation 6.19 will be employed in the next chapter when we identify a new property known as entropy . The reversed Carnot cycle (shown in Figure 6.16 with the directions of Q L and Q H reversed) can either represent a refrigeration or a heat pump cycle. The performance of a refrigerator is measured in terms of the coefficient of performance and for the refrigerator, the coefficient of performance was defined by Equations 3.19 and 6.4. For the heat pump, the coefficient of performance was defined by Equations 3.20 and 6.5. With Q L / Q H replaced by T L / T H in accordance with Equation 6.19 in Equations 6.4 and 6.5, we have for the Carnot refrigerator C = 1 T H T L − 1 (6.20) and for the Carnot heat pump C = 1 1 − T L T H (6.21) Example 6.5 A Carnot heat pump (Figure 6.17) supplies heat to a steam generator where water enters as saturated liquid at 100 kPa and exits as saturated vapor at the same pressure. The heat pump consumes 80 kW of power and draws heat from the environment at 10 ◦ C. Determine the rate of steam generation. 164 Introduction to Thermal and Fluid Engineering Saturated Vapor Saturated Liquid 100 kPa 100 kPa Steam Generator Heat Pump 80 kW 10°C (283 K) FIGURE 6.17 Configuration for Example 6.5. Solution Assumptions and Specifications (1) All processes in the cycle are internally reversible.
eBook - PDFStatistical and Thermal Physics
Fundamentals and Applications
- M.D. Sturge(Author)
- 2018(Publication Date)
- A K Peters/CRC Press(Publisher)
(15.9) 5 The nearest practical realization to the Carnot ideal gas cycle is the Stirling cycle; see, for example, P. C. Riedi, Thermal Physics (Oxford, 1988), p. 57. 15.1. The Carnot Engine 327 Figure 15.5. Slicing up an arbitrary cycle into in h nitesimal Carnot cycles. This is the area enclosed by the loop in the T -S diagram, and is equal to S dT . Example 15.1. (Cooling a Debye solid.) Suppose that you have a heat bath at a temperature T 1 which is su ciently low that the heat capacity of a certain insulating solid is given by Debye’s T 3 law (Equation (6.44)), and that you have designed an ideal Carnot refrigerator to cool the solid from T 1 to T 2 , where T 2 T 1 . The refrigerator discharges heat to the heat bath at T 1 . Calculate the work needed to cool 1 kmole of the solid from T 1 to T 2 . When the solid is at temperature T , the coe cient of performance of the refrigerator (de h ned as heat extracted for unit work in: see Footnote 3) is h c = T T 1 T . Hence, the work needed to remove heat ¯ dQ is ¯ dW = T 1 T T ¯ dQ . If the heat capacity is C ( T ), the change in temperature is dT = ¯ dQ C ( T ) . Hence, total work done is W = T 2 T 1 C ( T ) T 1 T T dT. From Equation (6.44) C ( T ) = AT 3 , where A = 12 4 5 R 0 3 D , which is con-stant. Hence W = A T 2 T 1 T 2 ( T 1 T 2 ) dT AT 4 1 12 , where we have neglected terms in T 3 2 and higher. 328 15. Heat Engines Figure 15.6. Schematic 4 ow diagram for a steam power generator. Full lines represent 4 uid 4 ow; double lines represent power transmission. T = turbine, P = pump, LP = low pressure, HP = high pressure. The letters b through e refer to points on the cycle (see Figure 15.7 ). 15.2 The Steam Engine Most of the electrical generation in industrialized countries is powered by steam turbines, although the fuel (coal, oil, gas, or nuclear) may vary. The 4 ow diagram for a steam power station is shown schematically in Figure 15.6.
eBook - PDF- Sigurd Skogestad(Author)
- 2008(Publication Date)
- CRC Press(Publisher)
Furthermore, from the first law of thermodynamics (8.2), | W | = | Q H | − | Q C | and (8.3) gives for an ideal (reversible) cycle parenleftbigg | W | | Q H | parenrightbigg rev = T H − T C T H = 1 − T C T H (8.4) which is always between 0 (for T H = T C ) and 1 (for T H ≫ T L ). This is also known as the Carnot factor or Carnot “efficiency,” 3 η Carnot = 1 − T C T H (8.5) To maximize the theoretical fraction of heat | Q H | that can be converted to work | W | , we want T H to be as high as possible and than T c as low as possible, corresponding to a Carnot factor close to 1. These results, which originate from the study of steam engines, are extremely fundamental and form the historical basis for thermodynamics as a subject. Alternatively, if we have available a lot of heat and the cooling capacity Q C is limited, then the following ratio is of interest, parenleftbigg | W | | Q C | parenrightbigg rev = T H − T C T C = T H T C − 1 (8.6) which is always between 0 (for T H = T C ) and infinity (for T H ≫ T C ). Again, we find that we can extract more work when there is a large temperature difference between the hot and cold reservoirs. Note. It is emphasized that one must always use the absolute temperature T [K] when calculating the Carnot factor. 3 I am not very happy about the commonly used term “Carnot efficiency,” because an efficiency should – in my opinion – be 1 for an ideal (reversible) process. I therefore recommend using the term “Carnot factor;” more about this on page 211. WORK FROM HEAT 201 Example 8.1 Arctic versus tropical cooling water. We have available a heat reservoir at 400 o C and a cold “tropical” reservoir (cooling) at 25 o C. How much heat can be extracted as work? What is the answer if we instead have “arctic” cooling at 5 o C? In the case with cooling at 25 o C (tropical conditions), the Carnot factor is η = | W rev | | Q H | = 1 − T C T H = 1 − 298 673 = 0 . 557 that is, 55.7% of the heat can in theory be removed as work.
- John Reisel(Author)
- 2021(Publication Date)
- Cengage Learning EMEA(Publisher)
Similarly, the increase in entropy in the pump makes the cycle less ideal; however, the left-hand side of the T-s diagram of the cycle was already considerably different from the rectangle in the Carnot cycle, and the small difference introduced by a nonisentropic pump is fairly insignificant. It is desirable to increase the thermal efficiency of steam power plants. As seen in Example 7.3, it is reasonable to expect that plants following a basic Rankine cycle with realistic components will have thermal efficiencies below 30%. The lower the thermal efficiency of a power plant, the more fuel that needs to be consumed in order to get the same net power output. Fuel costs money, and so it is desirable to have a higher thermal efficiency to save plant operators money on fuel costs. However, if we consider ourselves limited to the basic Rankine cycle using water, the highest temperature that could be achieved for the steam entering the turbine is the critical temperature of 374.148C (647 K). On the heat rejection side of the cycle, it is reasonable to expect that the heat will be rejected to the environment, and it is reasonable to consider a standard environmental temperature at 258C (298 K); the steam exiting the turbine and condensing in the condenser cannot be colder than the environment temperature if heat is to be transferred from the steam to the environment. A Carnot cycle operating between these two temperatures will have an efficiency of 0.539. This is a low maximum possible efficiency, and when we consider that the isentropic efficiency of a realistic turbine under these conditions will not be extremely high (due to the high moisture content of the flow of the steam through the turbine), it is reasonable to conclude that the best possible thermal efficiency that could be achieved with a realistic basic Rankine cycle in practice would be less than 40%, and likely even lower.
- Lucien Borel, Daniel Favrat(Authors)
- 2010(Publication Date)
- PPUR(Publisher)
13.13 A Stirling cycle operated with a perfect gas by means of the system of Figure 13.12. Thermodynamic cycles 629 • and path 4-1, corresponding to an isochoric cooling, with the elevation of the piston Pd, during which the gas flows again through the storage A, but this time from the top to the bottom, and gives to it heat , at a temperature varying from to . Note that the heat transfer of path 4-1 to path 2-3 is done with operations that are shifted in time, by intermediate storage, using the storage A. Theoretically, this transfer is characterized by the fact that the part of heat is given along the path 4-1 at a certain temperature T, stored in the storage A in the form of internal energy at the same temperature T, and received along the path 2-3, still at the same temperature T. It therefore consists of a reversible heat transfer. This is a limit, which implies in principle that the matter of the storage A has either an infinite mass, or an infinite specific heat and that it constantly has the same temperature gradient. Features The Stirling cycle has exactly the same features as the Carnot cycle. In particular, Relations (13.47) through (13.52) remain entirely valid. Hence, the Stirling cycle is characterized by the same power effectiveness and the same exergy effi- ciency as the Carnot cycle. 13.5.6 Ericsson cycle Definition An Ericsson cycle is a reversible bithermal power cycle, with internal heat trans- fer, comprised of two isothermal and of two isobaric processes. q i T h T a q i δq i ε m h ∗ = Θ η ∗ = 1 Fig. 13.14 A bithermal closed system, with the atmosphere as the cold source, and with fluid transfer and internal heat transfer, in steady-state operation. Cold source at T a (atmosphere) Hot source at T h Heated turbine Cooled compressor Heat exchanger Q h +
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