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.
7 Key excerpts on "Carnot Cycle"
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 - ePubEinstein's Fridge
The Science of Fire, Ice and the Universe
- Paul Sen(Author)
- 2020(Publication Date)
- William Collins(Publisher)
...If the cylinder was completely insulated – that is, adiabatic – the gas would cool. But as the cylinder is next to the furnace, heat will flow into it, compensating for any drop in temperature. So, as heat flows into the air, it expands, creating a quantity of motive power while its temperature remains unchanged. This is known as an isothermal expansion. For a given, fixed temperature, it creates the most motive power possible from a given amount of heat. Like the adiabatic process, the isothermal one can run backwards, too. In this case, you press down on a piston in a cylinder containing gas at the same temperature as an adjacent sink. The temperature does not rise as it would in the adiabatic case because as it starts to do so, the heat flows into the sink. This is known as isothermal compression. At a given, fixed temperature, this uses up the least amount of effort or motive power to compress a gas, while removing heat from it. With these two processes, adiabatic and isothermal, in mind, Carnot sketched the ideal, maximally efficient heat engine. The picture shows a single vertical cylinder containing a piston that moves up and down. Below it on the left is a furnace, labelled A, on the right a sink, labelled B. Heat is used to expand gas, and this pushes the piston directly. Carnot’s original diagram of an ideal engine. When the gas needs to be heated, the cylinder containing it is brought into contact with the furnace (A), and when the gas needs to be cooled, the cylinder moves across and is brought into contact with the sink (B). Carnot imagined the furnace to be so vast that no matter how much heat flows out of it, its temperature doesn’t fall. It remains at, say, T(furnace) degrees. Similarly, he imagined the sink to be so large that no matter how much heat flows into it, its temperature does not rise, remaining at, say, T(sink). Then Carnot describes how the engine functions...
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- Mike Pauken(Author)
- 2011(Publication Date)
- For Dummies(Publisher)
...These processes are heat input, heat rejection, work input, and work output. Take your automobile engine as an example of a heat engine. Here are the four basic processes that go on under the hood: Work input Air is compressed in the cylinders. This compression requires work from the engine itself. Initially, this work comes from the starter. As you can imagine, this process takes a lot of work, which is why they don’t have those crank handles on the front of cars any more. Heat input Fuel is burned in the cylinder, where the heat is added to the engine. The heated air in the cylinder naturally wants to increase in pressure and expand. The pressure and expansion move the piston down the cylinder. Work output As the expanding gas in the cylinder pushes the piston, work is output by the engine. Some of this work compresses the air in adjacent cylinders. Heat rejection The last process removes heat with the exhaust from the engine. Refrigeration: Letting work move heat When Willis Carrier made air conditioners a popular home appliance, he did more than make people comfortable and give electric utilities a reason for growth and expansion. He brought thermodynamics into the home. Thermo-dynamics has been there all along, and you never realized it. Refrigerators, freezers, air conditioners, and heat pumps are all the same in thermodynamics. Only three basic processes involve energy interacting with the surroundings in what is known as the refrigeration cycle: Heat input Heat is absorbed from the cold space to keep it cold. Work input Work is added to the system to pump the heat absorbed from the cold space out to the hot space. Heat rejection Heat is rejected to the hot space. Actually, a fourth process takes place in most refrigeration cycles, but it doesn’t involve a change in energy. Instead of having a work-output process in the cycle like heat engines do, refrigerators simply utilize a pressure-reducing device in the system...
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...
