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.
7 Key excerpts on "Carnot Vapor Cycle"
eBook - ePubMeasurement, Quantification and Economic Analysis
Numeracy in Economics
- Ingrid H. Rima, Ingrid H. Rima(Authors)
- 2002(Publication Date)
- Routledge(Publisher)
...To understand human actions in this light, we first review the physics of the Carnot engine. Then we consider an individual in a similar closed path in real time over a utility field. We then extend the analysis to the labor and capital cycles in reversible and irreversible form. THE REVERSIBLE CARNOT ENGINE IN THE MECHANICAL PLANE The Carnot engine was an idealized steam engine. Abstraction from the “historical” dissipative effects of friction, leakage and wear and tear made it reversible. It could be driven backward, so the parameters describing its state would recover their original values at the end of each cycle (Zemansky 1957; Truesdell 1980). 4 Gas (steam) is enclosed in a cylinder and held under pressure by a piston, which is coupled to a mechanical device such as the flywheel in Figure 16.1. Mechanical work is done as the injection of heat causes the gas to expand, driving the piston and the flywheel. 5 Cooling the gas returns the piston to its original position, permitting the cycle to be repeated. The principles that make the engine work are the first and second laws of thermodynamics. The first law is the conservation of energy E. It is nothing but the statement that E is a state variable, a scalar function of temperature T, pressure P and volume V. A closed loop in these values implies zero net change in E over the cycle no matter how rapidly or long the machine has operated. The heat Q, and work W, transferred by the engine do not describe the state of the engine at an instant of time, but rather the flows of energy it imports and exports over time. Flows are not conserved, but depend on the path of the state parameters as the machine operates. The change in the state variable E is the algebraic sum of the flows of heat and work. 6 Since the change in E is zero over the closed cycle, the flow of heat applied is equal and opposite to the work performed...
eBook - ePubStirling Cycle Engines
Inner Workings and Design
- Allan J. Organ(Author)
- 2013(Publication Date)
- Wiley(Publisher)
...2 Réflexions sur le cicle de Carnot 2.1 Background There are few written accounts of the Stirling engine which fail to mention the ideal Carnot 1 cycle. The purpose of inclusion is to compare its efficiency η C = 1 − T C /T E with the efficiency potential of the practical Stirling engine. Chapter 1 has already drawn attention to a spurious comparison. If the objection needed strengthening: The Stirling engine is a viable prime mover. The Carnot cycle is an abstraction which has yet to demonstrate that it can make a living turning a crank. It is difficult to conceive of a practical embodiment of the Carnot cycle having any chance of approaching its own limiting efficiency. Constructed from conventional materials it would be crippled by thermal diffusion or by sealing problems – or by both. The original proposition (Carnot 1824) envisages a reciprocating embodiment. The gas process sequence described by Carnot does not define a closed cycle. Follow-up accounts overlook this aspect, dwelling instead on the indicator diagram. The latter has gained a reputation for an unfavourable ratio of p-V area to peak pressure. There is, however, no unique indicator diagram, which instead is a function of no fewer than three independent dimensionless parameters: temperature ratio N T = T E / T C, specific heat ratio γ, and compression ratio r v = V 1 / V 3. Shape and mean effective pressure vary markedly depending on the combination of numerical values. This writer has yet to come across a second-hand account of the Carnot cycle referring to anything deeper than the usual arbitrary quartet of intersecting isotherms and adiabats. Putting the Carnot/Stirling comparison onto a sounder footing will mean re-visiting the ideal Carnot cycle. Taking things a step closer to the reality of a Carnot ‘engine’ will have insights for other externally heated reciprocating prime movers – Stirling, thermal lag, and so on. 2.2 Carnot re-visited The ideal Carnot cycle is universally taken for granted...
eBook - ePub- Tangellapalli Srinivas(Author)
- 2021(Publication Date)
- Bentham Science Publishers(Publisher)
...The Kelvin-Plank (KP), states that it is impossible to construct a heat engine that executes heat with single TER. If an engine working with single TER, that engine is called perpetual motion machine of second kind (PMM 2). Therefore, PMM 2 is impossible. Clausius conceptualized the second law of thermodynamics based on the heat pump working. As per the Clausius statement, it is impossible to construct a heat pump or refrigerator that removes the heat from a body at lower temperature to a body at high temperature without using work. CARNOT CYCLE A standard heat engine or a heat pump is required to estimate the maximum gain from thermal machines. Carnot machine is such an imaginary or hypothetical machine shown as a master piece. Carnot cycle is a reversible cycle consists of four processes as shown in Fig. (1). Fig. (1)) Representation of Carnot engine on (a) P-V diagram and (b) T-s diagram. 1) Reversible isothermal process (1-2) Heat is added at constant temperature process. (8) (9) 2) Isentropic expansion process (2-3) 0 = (U 3 - U 2) + W 2-3 3) Isothermal process (3-4) Heat is rejected at isothermal process 4) Isentropic compression process (4-1) 0 = (U 1 - U 4) - W 4-1 For Carnot power cycle, (10) Or, Similarly, for Carnot refrigeration cycle, (11) ENTROPY The word entropy was first used by Clausius, taken from the Greek word ‘tropee’ meaning ‘transformation’. Entropy is the fourth property (dimension) in thermodynamics after pressure, volume and temperature. Pressure, volume and temperature are the properties can be measured with the instruments but entropy cannot be measured using instrument and so it a special property. Actually it brings a new look to thermodynamics as it adds the quality to the energy...
eBook - ePubEssentials of Energy Technology
Sources, Transport, Storage, Conservation
- Jochen Fricke, Walter L. Borst(Authors)
- 2013(Publication Date)
- Wiley-VCH(Publisher)
...The efficiency η C in Eq. (3.1) is defined as the work W divided by the provided heat Q 34. Applying the first law of thermodynamics (conservation of energy), we know that 3.2 and we obtain 3.3 Problem 3.1 Derive Eq. (3.1) from the TS diagram in Figure 3.2. Problem 3.2 Find out from suitable sources whether or not the Carnot cycle was ever put to use. Problem 3.3 Calculate the Carnot efficiency for conversion of heat into work for a temperature T c = 300 K of the cold reservoir and temperatures T h = 400, 600, 1200 K of the hot reservoir. 3.2 Stirling Engine Another important thermodynamic cycle was invented by the Reverend Dr. Robert Stirling. His engine was patented in 1816 and technically realized in 1818. It achieved efficiencies of about 18% in the nineteenth century. The pV and TS diagrams are shown in Figure 3.3. Figure 3.3 Idealized Stirling cycle with two isothermal and two isochoric processes. The isothermal processes (3 → 4 and 1 → 2) are the same as in the Carnot process. The entropy changes from 4 → 1 and 2 → 3 are the same in magnitude and opposite in sign and cancel. The efficiency of the ideal Stirling process is identical to the Carnot efficiency: 3.4 This follows from the identical isothermal expansion (3 → 4) and compression (1 → 2) routes for both cycles and the isochoric routes, which are adiabatic provided the displacement piston (Figure 3.4) is ideal. The piston has to store and transfer the thermal energy from the working fluid (gas) that is being shuttled between the warm and cold parts of the ideal engine with 100% efficiency. The thermal conductivity of the displacement piston or, more precisely, its thermal diffusivity should be high. Its flow resistance, however, must be small...
eBook - ePub- V. Babu(Author)
- 2019(Publication Date)
- CRC Press(Publisher)
...8.7. As the gas absorbs the heat, the piston moves outward causing the gas to expand slowly, and hence remain at the temperature T H (process 1-2 in Fig. 8.8). Once the desired amount of heat, Q H, has been transferred, the cylinder is kept on an insulated stand, where it undergoes further expansion, until its temperature decreases to the temperature of the cold reservoir, T C (process 2-3 in Fig. 8.8). The cylinder is then brought into contact with the cold reservoir in the same manner as before. The piston now starts moving inward in such as a manner as to compress the gas slowly so that the temperature remains constant (process 3-4 in Fig. 8.8). Once the required amount of heat, Q C, has been rejected to the cold reservoir, the cylinder is kept on the insulated stand. The gas is now compressed slowly until its temperature increases to that of the hot reservoir (process 4-1 in Fig. 8.8 and the entire sequence is repeated. Figure 8.8: Carnot cycle in P − v coordinates The Carnot engine described above is an appropriate idealization of heat engines in which the working substance undergoes non-flow processes. For instance, a single cylinder in the multi-cylinder engine shown in the top in Fig. 2.10 could be such a heat engine. However, the working substance undergoes steady flow processes in the heat engines described in section 8.2. A Carnot engine that is appropriate for such a situation will employ a reversible isothermal turbine, reversible adiabatic turbine, reversible isothermal compressor and a reversible adiabatic compressor to accomplish processes 1-2, 2-3, 3-4 and 4-1 in Fig. 8.8 respectively. The processes remain the same, as they should, since the arguments made at the beginning of this section in this connection are quite general. The realization of the device alone differs, depending on whether the processes that comprise the cycle are required to be flow or non-flow processes. If the direct Carnot cycle shown in Fig...
eBook - ePubGeothermal Heat Pumps
A Guide for Planning and Installing
- Karl Ochsner(Author)
- 2012(Publication Date)
- Routledge(Publisher)
...Therefore, more compression work is required in order to achieve the same end pressure and saturation temperature. The energy transferred in the cycle can be taken directly as the enthalpy differences from the h, lg p-diagram (Figure 2.6). The Carnot Efficiency can be quickly determined using these values: ε c = h2 – h3/h2 – h1 For actual processes, the COP may be determined as: ε c = h2* – h3*/h2* – h1* Cycle with super-heating and sub-cooling: 4* – 1 Evaporation, absorption of vaporization energy h1 – h4 1–1* Super-heating of intake gas 1* – 2* Compression to set compression temperature (super-heated refrigerant vapour) 2* – 2 Cooling to saturated vapour temperature, release of super-heating energy h2* – h2 2–3 Condensation, release of vaporization energy, h2* – h3 3–3* Sub-cooling of fluid 3* – 4* Expansion in the unsaturated vapor phase; no energy release (transformation from sensible to latent heat) Cycle without super-heating and sub-cooling: 4 – 1 – 2'– 3 – 4 2.7 Heat Pump Cycle with Injection Cooling In order to increase COP and heating capacity and to make a higher temperature-lift possible, heat pumps can be designed with injection cooling, e.g. air source heat pumps with vapour-injection – cooling can supply temperatures up to 65°C even in coldest climates. Figure 2.7 Refrigerant Cycle with Enhanced Vapour Injection Source: Copeland GmbH...
eBook - ePub- Mike Pauken(Author)
- 2011(Publication Date)
- For Dummies(Publisher)
...The steam can then be used in a power plant to generate additional electricity. The heat rejected by one heat engine can be the heat source for another heat engine operating at lower temperatures. (One man’s trash is another man’s treasure.) I describe cogeneration and combined cycles in a bit more detail in Chapter 18. Chilling with the Clausius Statement on Refrigeration Heat naturally flows from hot sources to cold sinks. Until the invention of the first refrigeration machine, you couldn’t do much about the natural flow of heat. You just had to sweat it out during the summer until winter came. All that has changed, but moving heat from a cold reservoir up to a warmer reservoir comes with a price, as you may know if you’ve paid a huge electric bill in the summer for air conditioning. Thermodynamically, a refrigerator is very much like a heat engine operating in reverse. It uses work to move heat from a low-temperature reservoir, such as the inside of your refrigerator, to a high-temperature reservoir, like your kitchen. Examples of refrigeration machines include air conditioners and heat pumps. A heat pump is basically an air conditioner that can pump heat from the outdoors to the inside of a house during the winter. It works best in areas with mild winters (I explain why in Chapter 13). The following sections discuss how the second law of thermodynamics applies to refrigeration cycles and provides a brief introduction on how the refrigeration cycle works. I go into more depth and discuss how to analyze refrigeration cycles in Chapter 13. Characterizing refrigerators Because heat naturally flows from hot to cold temperatures, making it flow in the opposite direction takes some effort. This observation is expressed as the Clausius statement of the second law of thermodynamics: It’s impossible for a refrigerator to move heat from a colder reservoir to a warmer reservoir without a work input...
