Reversible Carnot Cycle Research Articles

The other half of the principle of heat-work conversion cycles: The theorem, principle and core physical quantity of reversed cycles

Engineering thermodynamics mainly focuses on the principles and methods for the heat-work conversion and to improve heat-work conversion efficiency. In current literatures, discussions are mainly focused on the heat-work cycles, which converts heat to work. Besides, the core physical quantity of heat-work cycles is entropy, which presents the heat-work conversion ability of the system. As for reversed cycles, the discussions are not quite detailed, and most of them applied the theory for heat-work cycles directly on reversed cycles. However, its well known that heat cannot be fully converted to work in a reversible thermodynamic cycle, which leads an efficiency less than 1. For reversed cycles, the heat output from the cycle can be much more than the net work the cycle costs, which derives a coefficient of performance (COP) more than 1. This phenomenon implies the principles of heat-work conversion in ordinary heat-work cycles and reversed cycles are somehow different, and some problems are naturally drawn as follows: (1) Is the COP of the reversed Carnot cycle the maximum possible COP for all reversed cycles within two temperature limits? (2) Heat can be judged from its quality, i.e. its temperature, and does the mechanical work have its quality? To answer these questions, this work analyzed and discussed the theorem, principle, and core physical quantity of reversed thermodynamic cycles. First, the principle for ordinary thermodynamic cycles are briefly reviewed, including the Carnot theorem and its proof, and the derivation of the concept of entropy from the Clausius original approach. Second, current conclusions of reversed cycles are reviewed and the air compression refrigeration cycle is taken as an example. The analysis comparing two cycles within given temperature limits presented that for given two temperature limits, the COP of the reversed Carnot cycle is the minimum possible COP, which is different from current conclusions. The quality of volumetric work is then discussed, and a new reversed cycle named reversed p-V cycle is proposed, which operates between two given pressure limits. The analysis indicates that this cycle is the best reversed cycle operating between two given pressure limits. Based on these discussion, the theorem and principle for reversed cycles corresponding to the second law and the Carnots theorem are derived and proved using the Clausius approach. The performance of the newly proposed reversed p-V cycle is investigated and compared with the reversed Carnot cycle operating within the same temperature limits, and results present that the COP of the reversed p-V cycle is much higher than the COP of the reversed Carnot cycle within the same temperature limits. Finally, from the equation of an arbitrary reversed cycle, it can be seen that the volume has a similar physical interpretation in the reversed cycles to the entropy in thermodynamic cycles, and it can be named as the work-entropy. In summary, the reversed cycles are analyzed, and its theorem, principles and core physical quantity are investigated.

Coefficient-of-Performance Analyses for Light-Emitting-Diode Cycles Resembling Carnot Heat Pumps

Designing the light-emitting diodes (LEDs) that yield maximal coefficients of performance ( ${\boldsymbol {\xi }}_{\boldsymbol {max}}$ ) subject to prescribed electrical powers constitutes a desirable and challenging task. In this paper, via an analogy between the reverse Carnot cycle and the LED cycle, we have identified two distinctive situations. Under normal operations, the electrical power is supplied to allow LED electrons to overcome the p/n junction barrier and is converted to thermal energy rate, which is dissipated to the surroundings. Meanwhile, the LED absorbs the very small amount of thermal energy rate (approximately zero and much smaller than the electrical power) from surroundings as a result of the Peltier effect. Therefore, the maximal light power emitted by the LED must not exceed electrical power ( $\boldsymbol {P}_{\boldsymbol {ele}}$ ) minus the barrier-overcoming power ( $\boldsymbol {I}\boldsymbol {V}_{\boldsymbol {net}}$ ). Subsequently, ${\boldsymbol {\xi }}_{\boldsymbol {max}}$ is obtained as $(\boldsymbol {P}_{\boldsymbol {ele}}-\boldsymbol {I}\boldsymbol {V}_{\boldsymbol {net}})/\boldsymbol {P}_{\boldsymbol {ele}}$ . Under relatively unusual situations when LEDs are capable of absorbing sufficient thermal energy rates from surrounding reservoirs (the same order of magnitude as the electrical power), ${\boldsymbol {\xi }}_{\boldsymbol {max}}$ can possibly exceed the unity, and its expression is theoretically derived in the text. Fundamentally, this paper may contribute to areas of energy saving and light-power illumination.

Performance investigation of a bi-functional integration system for power and heat supply

A novel bi-functional integration system for power and heat supply based on power generation technology and heat pump technology was proposed and designed in this paper, and the objective was to maximum energy efficiency with the exploitation of the waste heat source as much as possible. This system could be applied in low temperature waste heat recovery with a wide temperature range. In the experiment, a test bench for permanent magnet synchronous machine (PMSM) was built firstly to examine the performance that one PMSM could be a generator and electromotor. Based the first experimental results, the second test bench was built to investigate the performance of the bi-functional integration system using R142b as working fluid in different working conditions. The results indicated that the bi-functional integration system had good feasibility and stability in both reverse Carnot cycle (RCC) heat pump mode and organic Rankine cycle (ORC) power generation mode.

The performance analysis of reversed Carnot cycle and reversed <italic>p</italic>-<italic>V</italic> cycle

A reversed thermodynamic cycle is a cycle which consumes mechnical work and moves heat energy from a source with lower temperature to a source with higher temperature, and the coefficient of performance (COP) is generally applied to describe its performance. It has been widely accepted that within a certain temperature range, the reversed Carnot cycle has the best performance, i.e., it has the biggest COP. However, in this article it has been concluded that the COP of the reversed Carnot cycle is not the biggest within a certain temperature range from three different methods. Besides, a new reversed cycle is constructed in this article, which is called the reversed p - V cycle inspired by the derivation of Carnot cycle. The analysis presents that within the same temperature the COP of reversed p - V cycle is far larger than the COP of the reversed Carnot cycle. From this cycle it can be seen that the mechanical work also has the concept of quality, which is reflected by the pressure of the work source in the cycle.

Reversible and irreversible heat engine and refrigerator cycles

Although no reversible thermodynamic cycles exist in nature, nearly all cycles covered in textbooks are reversible. This is a review, clarification, and extension of results and concepts for quasistatic, reversible and irreversible processes and cycles, intended primarily for teachers and students. Distinctions between the latter process types are explained, with emphasis on clockwise (CW) and counterclockwise (CCW) cycles. Specific examples of each are examined, including Carnot, Kelvin and Stirling cycles. For the Stirling cycle, potentially useful task-specific efficiency measures are proposed and illustrated. Whether a cycle behaves as a traditional refrigerator or heat engine can depend on whether it is reversible or irreversible. Reversible and irreversible-quasistatic CW cycles both satisfy Carnot's inequality for thermal efficiency, η≤ηCarnot. Irreversible CCW cycles with two reservoirs satisfy the coefficient of performance inequality K≤KCarnot. However, an arbitrary reversible cycle satisfies K≥KCarnot when compared with a reversible Carnot cycle operating between its maximum and minimum temperatures, a potentially counterintuitive result.

Experimental study on a bifunctional heat utilization system of heat pump and power generation using low-grade heat source

This paper presents an experimental study on a heat utilization system functioning as power generation and heat pump. The power generation and heat pump functions are achieved on the discipline of organic Rankin cycle (ORC) and reverse Carnot cycle (RCC), respectively. In the experiment, an inverter scroll compressor has been modified to implement dual functions of expansion with power output in power generation mode and compression with power consumption in heat pump mode. The thermodynamic cycles is fed with HCFC-142b and recovering heat from low-grade heat source at temperatures ranging from 50 to 95°C. The results show good feasibility and stability of the bifunctional system under variable operating conditions. The performance of the bifunctional scroll machine is evaluated in terms of internal filling factor, isentropic efficiency and mechanical efficiency. In ORC power generation mode, the maximum power output is 2.95kW and thermal efficiency reaches a maximum value of 3.95% at optimal work condition. In heat pump mode, the water temperature at the evaporator inlet is fixed at about 50°C. The coefficient of performance (COP) ranges from 3.6 to 1.1 when the condensing temperature rises from 75 to 96°C.

The reversed chemical engine cycle with application to desalination processes

In this paper, a novel thermodynamic cycle is proposed, termed the reversed chemical engine cycle. In the cycle, a net input of work is used to transfer mass from a low chemical potential reservoir to a high chemical potential reservoir. The cycle has two mass exchangers, a pump and a turbine. The only irreversibility considered in the model is finite-rate mass transfer. Similar to the reversed Carnot cycle, expressions for the performance ratio (analogous to the coefficient of performance) are obtained under the condition of minimized power requirement for the endoreversible and, in turn, the reversible case. The reversed mass engine cycle is shown to be a special case of the reversed chemical engine. An equipartitioned hybrid forward osmosis reverse osmosis (FO–RO) system is considered as an example of the cycle.

Thermodynamic analysis of vapor compression heat pump cycle for tap water heating and development of CO2 heat pump water heater for residential use

The ideal vapor compression cycle for tap water heating and its coefficient of performance (COP) have been studied theoretically at first. The ideal cycle is defined as the cycle whose high temperature heat source varies temperature with constant specific heat and other processes are same as the reverse Carnot cycle. The COP upper limit of single stage compression heat pump cycle for tap water heating with various refrigerants such as fluorocarbons and natural refrigerants was calculated. The refrigerant which achieves the highest COP for supplying hot water is CO2. Next, the prototype of CO2 heat pump water heater for residential use has been developed. Its outline and experimental results are described. Finally its further possibility of COP improvement has been studied. The COP considered a limit from a technical point of view was estimated about 6.0 at the Japanese shoulder season (spring and autumn) test condition of heating water from 17°C to 65°C at 16°C heat source air temperature (dry bulb)/12°C (wet bulb).

Hourly Calculation Method of Air Source Heat Pump Behavior

The paper describes an hourly simplified model for the evaluation of the energy performance of heat pumps in cooling mode maintaining a high accuracy and low computational cost. This approach differs from the methods used for the assessment of the overall energy consumption of the building, normally placed in the so-called white or black box models, where the transient conduction equation is deterministically and stochastically solved, respectively. The present method wants to be the expression of the grey box model, taking place between the previous approaches. The building envelope is defined using a building thermal model realized with a 3 Resistance 1 Capacitance (3R1C) thermal network based on the solution of the lumped capacitance method. The simplified model evaluates the energy efficiency ratio (EER) of a heat pump through the determination of the hourly second law efficiency of a reversed Carnot cycle. The results of the simplified method were finally compared with those provided by EnergyPlus, a dynamic building energy simulation program, and those collected from an outdoor test cell in real working conditions. The results are presented in temperatures and energy consumptions profiles and are validated using the Bland-Altman test.

Grey-box modelling of a household refrigeration unit using time series data in application to demand side management

Abstract This paper describes the application of stochastic grey-box modelling to identify electrical power consumption-to-temperature models of a domestic freezer using experimental measurements. The models are formulated using stochastic differential equations (SDEs), estimated by maximum likelihood estimation (MLE), validated through the model residuals analysis and cross-validated to detect model over-fitting. A nonlinear model based on the reversed Carnot cycle is also presented and included in the modelling performance analysis. As an application of the models, we apply model predictive control (MPC) to shift the electricity consumption of a freezer in demand response experiments, thereby addressing the model selection problem also from the application point of view and showing in an experimental context the ability of MPC to exploit the freezer as a demand side resource (DSR).

Note on electrical and thermodynamic properties of isolated horizons

The electrical laws and Carnot cycle of Isolated Horizon (IH) are investigated in this paper. We establish the Ohm's law and Joule's law of an Isolated Horizon, and find that the conceptual picture of black holes (Membrane Paradigm) can also apply to this kind of quasi-local black holes. We also investigate the geometrical properties near a non-rotating IH, and find that under the first-order approximation of r, there exist a Killing vector and a Hamiltonian conjugate to it, so this vector is a physical observer. We calculate the energy as measured at infinity of a particle at rest outside a non-rotating IH, and use this result to construct a reversible Carnot cycle with the Isolated Horizon as a cold reservoir, which confirms the thermodynamic nature of Isolated Horizon.

Thermodynamic analysis of a novel energy-efficient refrigeration system subcooled by liquid desiccant dehumidification and evaporation

A new energy-efficient refrigeration system subcooled by liquid desiccant dehumidification and evaporation was proposed in this paper. In the system, liquid desiccant system could produce very dry air for an indirect evaporative cooler, which would subcool the vapor compression refrigeration system to get higher COP than conventional refrigeration system. The desiccant cooling system can use the condensation heat for the desiccant regeneration. Thermodynamic analysis is made to discuss the effects of operation parameters (condensing temperature, liquid desiccant concentration, ambient air temperature and relative humidity) on the system performance. Results show that the proposed hybrid vapor compression refrigeration system achieves significantly higher COP than conventional vapor compression refrigeration system, and even higher than the reverse Carnot cycle at the same operation conditions. The maximum COPs of the hybrid systems using hot air and ambient air are 18.8% and 16.3% higher than that of the conventional vapor compression refrigeration system under varied conditions, respectively.

An effective thermodynamic transformation analysis method for actual irreversible cycle

An effective thermodynamic transformation analysis method was proposed in this study. According to the phenomenon of exergy consumption always coupling with heat transfer process, the effective thermodynamic temperatures were defined, then the actual power cycle or refrigeration/heat pump cycle was transformed into the equivalent reversible Carnot or reverse Carnot cycles for thermodynamic analysis. The derived effective thermodynamic temperature of the hot reservoir of the equivalent reverse Carnot cycle is the basis of the proposed method. The combined diagram of TR-h and TR-q was adopted for the analysis of the system performance and the exergy consumption, which takes advantage of the visual expression of the heat/work exchange and the enthalpy change, and is convenient for the calculation of the coefficient of performance and exergy consumptions. Take a heat pump water heater with refrigerant of R22 for example, the proposed method was systematically introduced, and the fitting formulas of the effective thermodynamic temperatures were given as demonstration. The results show that the proposed method has advantage and well application foreground in the performance simulation and estimation under the variable working conditions.

A novel approach to design and fabrication of thermo-acoustic refrigerator using high amplitude sound waves

The basic object of this paper is compression of refrigerant by the consumption of high amplitude sound waves that results the generation thermal Energy. For generation of sound waves a loud speaker (or common audio speaker) has been employed for creating high amplitude sound waves which compresses refrigerant (helium) by the well Known thermodynamics process of heat absorption. A Thermo acoustic refrigerator is fabricated with a cooler and loud speaker. The acoustic power produced by a loud speaker as a sound waves reaches to heat the pump. The cooler works on a reverse Carnot cycle by incorporating a compact acoustic network to create the travelling wave phasing necessary to operate. As the acoustic wave propagates temperature difference occurs at the ends of stack, heat and cold is trap by the heat exchangers regenerator from a cold heat exchanger to an ambient one. Instead of using co-axial topology network, the toroidal is used. The design, construction and performance measurement of the cooler are also discussed. Finally, at 8 0 C a

Optimization of Combine Heat Pump and Cogeneration System under Alternative Performance Criteria

In this study, a performance analysis based on alternative performance criteria has been performed for a reversible Carnot and heat pump cycle, modified for cogeneration, with external irreversibilities. The optimum values of the design parameters of the new cogeneration cycle were determined for different criteria. In this context, the effects of design parameters on the exergetic performance are investigated, and the results are discussed. The obtained results may guide towards a more realistic criterion for actual combine heat pump and cogeneration plants.

Cooling Process after HTST Orange Juice Sterilization Optimization Based on CFD

In order to study the juice cooling process after sterilization to obtain the accurate process and reduce the energy used in the cooling, the orange juice in can high temperature short time (HTST) sterilization process was calculated. The maximum temperature of juice in can was defined as 60°C. By using FLUENT, a kind of software which combines hydrodynamics, mathematics and computer technology, we were able to put different fluids into analog computation and numerical experiment to solve problems related to hydrodynamics. Orange juice cooling numerical experiment after HTST sterilization was carried out. The optimization cooling process was obtained: 20°C(293K),14 minutes;15°C(288K),13 minutes; 10°C(283K) ,13minutes; 5°C(278K), 12minutes and 0°C(273K), 12minutes. Using Carnot efficiency in Reverse Carnot cycle, the energy consumption was: 288W, 325W, 348W, 391W, 417W in accordance. And in the result, the optimized process was : 20°C(293K),12 minutes.

Irreversible cycle in linear irreversible thermodynamics

The reversible Carnot cycle in reversible thermodynamics is composed of two reversible heat exchange processes and two reversible adiabatic processes. We construct an irreversible cycle in linear irreversible thermodynamics by analogy with the reversible Carnot cycle. The irreversible cycle is composed of two linear irreversible heat exchange processes and two linear irreversible adiabatic processes. It is found that the Curzon–Alhborn efficiency can be attained if the power for each of the four linear irreversible processes reaches its maximum. The maximum efficiency is the Carnot efficiency. The strong coupling condition is prerequisite for the respective attainment of the Curzon–Alhborn efficiency and the Carnot efficiency.

Reversible Carnot cycle outside a black hole

A Carnot cycle outside a Schwarzschild black hole is investigated in detail. We propose a reversible Carnot cycle with a black hole being the cold reservoir. In our model, a Carnot engine operates between a hot reservoir with temperature T1 and a black hole with Hawking temperature TH. By naturally extending the ordinary Carnot cycle to the black hole system, we show that the thermal efficiency for a reversible process can reach the maximal efficiency 1 – TH/T1. Consequently, black holes can be used to determine the thermodynamic temperature by means of the Carnot cycle. The role of the atmosphere around the black hole is discussed. We show that the thermal atmosphere provides a necessary mechanism to make the process reversible.

Derivation of Ideal Heat Pump Cycle for Hot Water Supply and Its COP and Evaluation of Hopeful Refrigerant

The reverse Carnot cycle, the high and low heat source of which are constant temperatures, decides the theoretical limit of COP of conventional heat pumps used as air conditioners etc. But the cycle which decides the theoretical limit of COP of a heat pump used as tap water heater is defined as the cycle whose high heat source varies temperature with constant specific heat, because the specific heat of tap water is constant and tap water heating with high temperature rise is needed. In this paper, the COP of this ideal cycle is clarified. And upper limit of COP of heat pump cycle with various refrigerants for tap water heating is studied and finally the refrigerant which achieves the highest COP for supplying hot water is clarified.

A new performance criterion for heat engines: efficient power

AbstractMany performance analyses have been carried out based on two comparative criteria namely maximum power (mp) and maximum power density (mpd). Researchers involved in power maximization studies have utilized the thermal efficiency at mp (Curzon–Ahlborn efficiency) as an efficiency standard for practical heat engines. On the other hand, maximum power density studies showed that the efficiency at mpd is always greater than that at the mp, while the power output from heat engines reduces. In this study, a new performance analysis is applied to a reversible Carnot cycle based on a new criterion which is proposed for all kind of heat engines. The proposed criterion, called efficient power, is defined as the multiplication of power by efficiency. This criterion considers not only the power output, but also the cycle efficiency. Maximizing the efficient power gives a compromise between power and efficiency. The results showed that the design parameters at maximum efficient power (mep) conditions lead to mo...