Technology & Engineering
Carnot Cycle
The Carnot cycle is a theoretical thermodynamic cycle that represents the most efficient process possible for converting heat into work. It consists of four reversible processes: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression. The Carnot cycle serves as a benchmark for the maximum efficiency that any heat engine can achieve.
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eBook - PDFThermodynamics
A Smart Approach
- Ibrahim Dinçer(Author)
- 2020(Publication Date)
- Wiley(Publisher)
The power cycles can be categorized based on the phase of the working fluid; they are either gas cycles and vapor cycles. Gas cycles are those thermodynamic cycles in which the working fluid remains throughout the cycle in the gaseous phase, while in vapor cycles the working fluid changes phase between the vapor and liquid phases throughout the cycle. This chapter introduces each cycle and the balance equations of that cycle and describes how these equations are used to investigate the cycle and assess its performance using the energy and exergy efficiencies. 6.2 Carnot Concept for Power Generation Further to our earlier discussion, the Carnot is technically a concept, although it is treated as a cycle by many; it is usually confused in many thermodynamics lectures. The Carnot con-cept is basically the concept of ideality and shows the maximum potential performance a power engine or a thermodynamics cycle can achieve. It essentially gives us the limits. In order to clearly illustrate how the principle of the Carnot concept is applied to power gen-eration cycles, especially the internal combustion cycles that can be approximated as pis-ton – cylinder devices, these cycles will be introduced one by one throughout the chapter. The result of the application of the Carnot concept on the previously mentioned power cycle is a Carnot Cycle that results in the highest efficiency of any cycles of heat engines. This comes as the Carnot Cycle neglects all irreversibility ’ s such as friction, heat losses, etc. This makes the Carnot Cycle a completely reversible cycle Figure 6.1 shows multiple illustrations of the Carnot Cycle using an ideal piston and its P-v and T-s diagrams as applied to heat engines in general. The Carnot Cycle consists of the following processes: • Reversible isothermal expansion (process 1-2): This is a process where the gas absorbs thermal energy q in and expands at a constant temperature T H .
eBook - PDFThermodynamics
From Concepts to Applications, Second Edition
- Arthur Shavit, Chaim Gutfinger(Authors)
- 2008(Publication Date)
- CRC Press(Publisher)
271 11 Power and Refrigeration Cycles In Chapters 7 and 8, it was established that to generate power by a heat engine at least two heat reservoirs at different temperatures are needed. The efficiency of power generation was shown to depend on the temperatures of the reservoirs, and on the type of engine that operates between them. In Chapter 7, we also introduced the concept of a Carnot engine which used an ideal gas as a working fluid. It was shown that the efficiency of that engine is the highest pos-sible obtained for an engine operating between two given reservoirs. In reality, an ideal gas Carnot engine is not a practical engine. Firstly it is difficult to build an engine that alternates between adiabatic and isothermal processes. Furthermore, the net work of this engine is obtained as a difference between two large quantities, the expansion work and the compression work. The isentropic efficiencies of expansion and compression in real engines are less than one. The net work is, therefore, considerably reduced and the effi-ciency of the cycle becomes quite low. A Carnot engine with a condensable vapor can overcome some of the problems men-tioned above. A T – s diagram for such an engine is shown in Figure 11.1. The isotherms in the two-phase region describe constant-pressure processes, which can be more easily accomplished in a practical system. Moreover, the work of compression is much lower than that of expansion, and thus the net work is less affected by the reduced isentropic efficiency. An example of a physical system that accomplishes such a cycle is shown schematically in Figure 11.2. 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.
eBook - PDF- Claus Borgnakke, Richard E. Sonntag(Authors)
- 2019(Publication Date)
- Wiley(Publisher)
Since we do not generally have constant temperature energy sources and sinks (reservoirs), it becomes difficult to implement the two isothermal processes except in the case of a phase change, shown in Fig. 5.18. These and other similar complexities will be mentioned in Chapters 9 and 10 for the cycles used in the real heat engines and refrigerators. For now, we can think of these energy conversion cycles as having a Carnot Cycle device as the best possible machine working between the two constant temperature reservoirs, which the next section will demonstrate. 5.6 TWO PROPOSITIONS REGARDING THE EFFICIENCY OF A Carnot Cycle There are two important propositions regarding the efficiency of a Carnot Cycle. First Proposition It is impossible to construct an engine that operates between two given reservoirs and is more efficient than a reversible engine operating between the same two reservoirs. Proposition I: any ≤ rev ......................................................................................................... .............. ....................................................... 158 CHAPTER FIVE THE SECOND LAW OF THERMODYNAMICS The proof of this statement is provided by a thought experiment. An initial assumption is made, and it is then shown that this assumption leads to impossible conclusions. The only possible conclusion is that the initial assumption was incorrect. Let us assume that there is an irreversible engine operating between two given reser- voirs that has a greater efficiency than a reversible engine operating between the same two reservoirs. Let the heat transfer to the irreversible engine be Q H , the heat rejected be Q ′ L , and the work be W IE (which equals Q H − Q ′ L ), as shown in Fig. 5.20. Let the reversible engine operate as a refrigerator (this is possible since it is reversible).
No longer available |Learn more- Irving Granet, Maurice Bluestein(Authors)
- 2014(Publication Date)
- CRC Press(Publisher)
This is because the Carnot Cycle requires constant temperature heat addition and rejection, which can be achieved by adding heat during the saturated (wet) mixture phase, causing evaporation, and removing heat during a wet mixture phase, causing condensation. Both of these processes occur at constant tem-perature. The line A , B represents the isentropic compression of the fluid from the lower temperature (and pressure) to the upper temperature of the cycle. At the upper tempera-ture, there is an isothermal and reversible reception of energy as heat from some reservoir. 375 Vapor Power Cycles This transfer of the heat proceeds along path B , C with concurrent increase in the volume of the vapor. The fluid then expands isentropically along path C , D with energy extracted as work. As the fluid expands, the volume of the fluid increases. Finally, the wet fluid is condensed isothermally and reversibly at the lower temperature of the cycle. During the condensation process, the volume of the fluid decreases as heat is rejected to the sink of the system. The energy available is represented by area A , B, C, D, and the energy rejected is represented by area A’, A , D, D ’ on the T – s diagram in Figure 8.1a. The efficiency of a Carnot Cycle is solely a function of the upper and lower temperatures and is given by η c = -× T T T 1 2 1 100 (8.1) Equation 8.1 is also the efficiency of any reversible heat engine operating between these constant temperature limits. All the heat is taken in or rejected at T 1 and T 2 , respectively. 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.
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- S. C. McBirnie(Author)
- 2013(Publication Date)
- Butterworth-Heinemann(Publisher)
S o m e conception of the requirements of such a cycle can be had by reference to the diagram in Figure 9.23. 404 STEAM-ENGINE AND TURBINE CYCLES AND EFFICIENCIES Thus, the irreversible reception of sensible heat in the boiler is replaced by a reversible operation, and the Carnot efficiency attained in consequence. This cycle in no way contravenes Carnot's principle, which makes reference only to reversibility and temperature limits. On the Ts diagram the single adiabatic CD is replaced by the curve CD 1 , which is in fact a series of infinitesimally small adiabatics moving progressively to the left. The simplified sketch is shown in Figure 9.24. Such a complete regenerative cycle is utterly impossible in practice. We cannot make an infinite number of feed-heating stages. Nor can we make heat flow from steam into water without a finite temperature difference between the two. The regenerative cycle is nevertheless the basis of the modern partial-regenerative cycle, with up to nine stages of feed heating by steam extracted from the engine or turbine, as described in Chapter 11 (see also Figure 9.25). Further work done on the partial-regenerative cycle in Chapter 11 will be illustrated by an enthalpy entropy dia-gram, as the calculation of such a cycle on a Ts diagram can become very tedious. The three shaded areas on the right-hand side of the dia-gram in Figure 9.25 must be transferred to the left-hand side, and on a Ts diagram this can involve a great deal of repetitive calculation. Figure 9.24 Regenerative cycle 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 4 0 5 Conclusions The following must be clearly understood: Once one of the above cycles is chosen, and its steam con-ditions fixed, then the above efficiency is the maximum thermal efficiency which can be attained. This is dependent only on the thermodynamical characteristics of the changes which take place in the steam.
No longer available |Learn moreAdvanced Thermodynamics
Fundamentals, Mathematics, Applications
- Mehrzad Tabatabaian, R. K. Rajput(Authors)
- 2017(Publication Date)
- Mercury Learning and Information(Publisher)
C H A P T E R 11 GAS POWER CYCLES 11.1. Overview The gas power cycle has the advantage of a lack of phase change com- pared to water/steam plants, but at the cost of lower power capacity. Overall, a gas power plant requires less equipment and is easier to start and stop in operation compared to steam power plants. In this chapter we discuss several gas power cycles. 11.2. Definition of a Cycle A cycle is defined as a repeated series of thermodynamic operations or processes occurring in a certain order. The processes may be repeated in the same order. The cycle may be of an imaginary perfect engine or an actual engine. The former is called an ideal cycle and the latter an actual cycle. In an ideal cycle all accidental heat losses and irreversibility are absent, and the working substance is assumed to behave like a perfect working substance. 11.3. Air Standard Efficiency To compare the effects of different cycles, it is of paramount importance that the effect of the calorific value of the fuel is altogether eliminated, and In This Chapter l Overview l Definition of a Cycle l Air Standard Efficiency l The Carnot Cycle l Otto Cycle l Exercises 510 • ADVANCED THERMODYNAMICS this can be achieved by considering air (which is assumed to behave as a perfect gas) as the working substance in the engine cylinder. The efficiency of an engine using air as the working medium is known as an Air standard efficiency. This efficiency is often called an ideal efficiency. The actual efficiency of a cycle is always less than the air standard efficiency of that cycle under ideal conditions. This is taken into account by introducing a new term, Relative efficiency, which is defined as: relative Actual thermal efficiency Air standard efficiency η = The analysis of all air standard cycles is based upon the following assumptions: 1. The gas in the engine cylinder is a perfect gas, that is, it obeys the ideal gas laws and has constant specific heats.
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.
- 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 +
eBook - PDFThermodynamics
Processes and Applications
- Jr. Logan, Jr., Earl Logan, Earl Logan Jr.(Authors)
- 1999(Publication Date)
- CRC Press(Publisher)
Determine the maximum work obtainable from the engine. 6.23 Two blocks of aluminum, each having a mass of 200 kg and a specific heat of 0.175 cal/g-°K, are initially at 1200 °K. Deter-mine the minimum work required of a reversed cycle engine, op-erating between the two blocks and receiving work from a MER, to lower the temperature of one of the blocks to 600°K. 166 Chapter 7 Chapter 7 Availability and Irreversibility 7.1 Available Energy The heat transfer process depicted in Figure 7.1 is accompanied by a rise in temperature and an increase in entropy. The rise of tem-perature means that the mass of the system receiving the energy is finite, i.e., it is not a reservoir. The heat addition is given by Qa = Jras (7.1) Figure 7.1 Available Energy Theoretically this heat transfer can be reversible if the system is placed in contact with an infinite number of reservoirs, each at a temperature which is exactly equal to the system temperature. For Availability and Irreversibility 167 such a reversible heat transfer there would be no change of en-tropy for the ensemble comprising the system and the TER sup-plying the energy. More realistically modeled the net entropy change would, of course, be positive. Another useful artifice is that of a Carnot engine which exe-cutes a cycle having an upper temperature equal to the temperature of the system at any value between T} and T2 and always discharg-ing energy as heat transfer to a TER at temperature T0. The col-lective work done is found by summing the infinitesimal quanti-ties produced during each cycle as the upper temperature of the Carnot Cycle varies from T{ to T2. The area under the process curve 1-2 in Figure 7.1 represents the transferred heat QA. The heat rejected QR by the Carnot engine is represented by the area T0AS, where AS is the entropy change from state 1 to state 2. The net work done by the engine is the same as the net heat transfer, viz., Q a - Qr .
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