Reversible Heat Engine Research Articles

Heat engines with finite reservoirs

Typical textbook analyses of heat engines assume that the temperatures of thermal reservoirs do not change; that is, the reservoirs have infinite heat capacity. Several authors have investigated the performance of reversible heat engines for which reservoirs have finite heat capacities and thus the reservoir temperatures do change with time. We find that previous studies have been too restrictive in that they assumed that the reservoir temperature change per cycle is infinitesimal and that the engine ceases operation when the hot reservoir cools to match the temperature of the cold reservoir. We model a Carnot-like engine and show that (1) the problem can be solved exactly with no requirement for infinitesimal temperature changes and (2) there is nothing special about the instant when the temperatures converge, with the device transitioning smoothly from a heat engine to a refrigerator. We find explicit expressions for the limiting reservoir temperature and the total efficiency.

Quantum thermal machines and batteries

The seminal work by Sadi Carnot in the early nineteenth century provided the blueprint of a reversible heat engine and the celebrated second law of thermodynamics eventually followed. Almost two centuries later, the quest to formulate a quantum theory of the thermodynamic laws has thus unsurprisingly motivated physicists to visualise what are known as `quantum thermal machines' (QTMs). In this article, we review the prominent developments achieved in the theoretical construction as well as understanding of QTMs, beginning from the formulation of their earliest prototypes to recent models. We also present a detailed introduction and highlight recent progress in the rapidly developing field of `quantum batteries'.

An Irreversible Heat Engine Working at the Reversible Efficiency

The thermodynamic analysis of the coupling of one cycle in the operation of a reversible heat engine with a work-degrading step in which the whole of the engine’s work output is frictionally degraded into heat at the temperature of its cold reservoir, allows identification of the fact that the engine’s reversibility is dependent on the continued availability of its work output. As long as this work remains available the engine will be reversible, this on reason of the fact that the initial condition can be restored via the simple expedient of using the said work to propel the inverse cycle. The moment this work becomes, for whatever reason, unavailable, restoration of the engine’s initial condition becomes impossible, and what was a reversible engine becomes irreversible. The inability of current thermodynamic terminology to deal with this situation is brought to light and a simple suggestion aimed at correcting this deficiency is advanced.

Reversible Carnot and Philips heat engines with a real gas as a working body

In the article, on the basis of the theory of thermodynamic potentials, a study was made of the quasistatic Phillips and Carnot heat engines in which a comparative analysis was made of their work both for cycles with a working body, an ideal gas, and for cycles with a working body, real gas. On the basis of the conducted research, it was established that the existing formulation of the Carnot theorem is valid only for the working fluid “ideal gas”. In general, based on the above calculations, the Carnot theorem can be formulated, for example, like this: “The efficiency of a reversible heat engine is maximum, does not depend on the properties of the heat engine and is a function of the temperatures of only hot and cold tanks: η=1- ƒ (t 1 ,t 2 ), where ƒ (t 1 ,t 2 ) is a function only of the temperatures t 1 and t 2 of the hot and cold tanks. This formulation is valid only for working fluid ideal gas. In the case of using real gas as a working fluid, the efficiency of a heat engine, in addition to dependence on the temperatures of hot and cold tanks, is a function of the thermodynamic characteristics of the working fluid and the type of heat engine, and reaches its maximum value for this type of working fluid and engine type if there is reversibility the system under consideration».

Regarding the application limitations of the Carnot, s theorem

The purpose of this article is to perform a comparative study of a reversible heat engine with an ideal or real gas as a working fluid and to determine the change in its efficiency depending on the thermodynamic characteristics of the working fluid. The main research method is the method of thermodynamic potentials, based primarily on the analysis of changes in the free and internal energy of an ideal and real gas in a cyclic process. The theory of thermodynamic potentials is used to consider the Carnot quasistatic heat engine. A comparative analysis of its operation is carried out, for a cycle with both an ideal and a real gas as a working fluid. The possibility of analyzing cyclic processes occurring in heat engines using the method of thermodynamic potentials has been identified and substantiated. The study has shown that the existing formulation of the Carnot’s theorem is valid only for ideal gas as a working fluid. Based on the work carried out, the Carnot’s theorem in the general case can be formulated, for example, as follows: the efficiency of the heat engine ηr, when it operates at the reversible Carnot cycle with real gas as a working fluid, is determined by the following expression:hr= 1 - TB /TA + ε,where TA and TB are the temperatures of the upper and lower isotherms of the Carnot cycle, respectively; ε is the correction term (positive or negative), depending on the thermodynamic properties of a real gas, which tends to zero as the properties of a real gas approach the properties of an ideal gas.

Thermo-Economic Optimization of an Idealized Solar Tower Power Plant Combined with MED System.

Based on the reversible heat engine model, theoretical analysis is carried out for economic performance of a solar tower power plant (STPP) combined with multi-effect desalination (MED). Taking total revenue of the output power and the fresh water yield per unit investment cost as the economic objective function, the most economical working condition of the system is given by analyzing the influence of the system investment composition, the receiver operating temperature, the concentration ratio, the efficiency of the endoreversible heat engine, and the relative water price on the economic parameters of the system. The variation curves of the economic objective function are given out when the main parameter is changed. The results show that the ratio of water price to electricity price, or relative price index, has a significant impact on system economy. When the water price is relatively low, with the effect numbers of the desalination system increasing, and the economic efficiency of the overall system worsens. Only when the price of fresh water rises to a certain value does it make sense to increase the effect. Additionally, the threshold of the fresh water price to the electricity price ratio is 0.22. Under the conditions of the current price index and the heliostat (or reflector), the cost ratio and the system economy can be maximized by selecting the optimum receiver temperature, the endoreversible heat engine efficiency, and the optimum concentration ratio. Given the receiver surface temperature and the endoreversible heat engine efficiency, increasing the system concentration ratio of the heliostat will be in favor of the system economy.

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.

Preparation and performance study of Er2O3 film selective thermal emitter

Solar thermophotovoltaic (STPV) generator is a popular energy converter due to providing low noise, low thermal mechanical stress and portability. It has the ability to exceed the efficiency of pure solar photovoltaic system. An idealized STPV generator is a reversible heat-engine, offering a theoretical efficiency of over 80%, but the actual conversion efficiency of STPV generator is still low due to the mistuned spectral property between the thermal selective emitter and the TPV cell. One key issue in developing the STPV generator with high performance is the spectral matching between the thermal radiation spectrum of radiator and the spectral response of photovoltaic cell in visible and near-infrared region, which usually lies between the visible and the near-infrared region. High-temperature spectral emissivity of rare earth oxide is of special interest, because the radiation has a narrow band of wavelengths in the near infrared and infrared region from 900 to 3000 nm. In this work, the thermal-selective film Er2O3 emitter is fabricated by post-oxidation of Er film deposited on Si substrate through using electron-beam gun evaporation. Based on the X-ray diffraction results, the Er2O3 film is of cubic phase structure and well-crystallized when the oxidation temperature is 700℃, and the Si substrate has no obvious influence on the crystal structure of Er2O3 film. According to the X-ray photoelectron spectroscopy results of the Er2O3 film after thermal oxidation at 700℃, the atomic ratio of Er/O is stoichiometric. In order to obtain the selective emission characteristic of the Er2O3 film, a measurement system is designed. The system consists of two major portions, i.e., one is a near infrared spectrometer purchased from Ocean Optics, the other is a high-temperature emission characteristic tester which can provide oxyhydrogen flame to heat the sample by using an electronic impulse ignition to torch the hydrogen-oxygen mixture. The oxyhydrogen flame passes through the nozzle and sprays vertically on the surface of the thermal-selective emitter sample. The facula of the oxyhydrogen flame convergence is very small (facula diameter:~0.8 cm), and the highest temperature achieved is about 2500℃. The measurement condition of selective emission performance of the Er2O3 film emitter coincides with the application characteristic of STPV generator. The emission performance result of the film emitter at 700℃ shows a typical gray-body emission characteristic. The measurements carried out at 900 and 1100℃ show that the Er2O3 film has a distinct emittance spectrum at 1550 nm corresponding to Er3+, and the intensity of the selective emission peak strengthens with the measuring temperature or film thickness increasing. The thermal-selective film Er2O3 emitter is found to have emission spectrum suitable for efficient matching with the infrared response of GaSb photovoltaic cell.

Total cost of operating an information engine

We study a two-level system controlled in a discrete feedback loop, modeling both the system and the controller in terms of stochastic Markov processes. We find that the extracted work, which is known to be bounded from above by the mutual information acquired during measurement, has to be compensated by an additional energy supply during the measurement process itself, which is bounded by the same mutual information from below. Our results confirm that the total cost of operating an information engine is in full agreement with the conventional second law of thermodynamics. We also consider the efficiency of the information engine as a function of the cycle time and discuss the operating condition for maximal power generation. Moreover, we find that the entropy production of our information engine is maximal for maximal efficiency, in sharp contrast to conventional reversible heat engines.

Reversible Heat Engines: Bounds on Estimated Efficiency from Inference

We consider work extraction from two finite reservoirs with constant heat capacity, when the thermodynamic coordinates of the process are not fully specified, i.e., are described by probabilities only. Incomplete information refers to both the specific value of the temperature as well as the label of the reservoir to which it is assigned. Based on the concept of inference, we characterize the reduced performance resulting from this lack of control. Indeed, the estimates for the average efficiency reveal that uncertainty regarding the exact labels reduces the maximal expected efficiency below the Carnot value (\(\eta _\mathrm{C}\)), its minimum value reproducing the well known Curzon–Ahlborn value: \(1-\sqrt{1-\eta _\mathrm{C}}\). We also estimate the efficiency before the value of the temperature is revealed. It is found that if the labels are known with certainty, then in the near-equilibrium limit the efficiency scales as \(\eta _\mathrm{C}/2\), while if there is maximal uncertainty in the labels, then the average estimate for efficiency drops to \(\eta _\mathrm{C}/3\). We also suggest how the inferred properties of the incomplete model can be mapped onto a model with complete information but with an additional source of thermodynamic irreversibility.

A Counterexample to the Second Law of Thermodynamics

The concatenation of one cycle in the operation of a reversible heat engine with that process in which the engine’s work output is irreversibly degraded into heat at the temperature of the cold reservoir, transforms the effects of the former into a couple of irreversible heat transfers. One of these heat transfers is found to be credited, via thermodynamic-sanctioned procedures, with two different entropy changes. A logical analysis centered on the principle of contradiction rejects one of these entropy changes as well as the thermodynamic notion leading to it. The rejected notion, the one assigning a zero entropy change to the heat-to-work transformation, brings to light a counterexample to the second law of thermodynamics in the form of an isothermal and reversible process with a different from zero total entropy change.

A note on the use of the temperature–entropy diagram in the proof of the second carnot theorem

A general graphical proof for the second Carnot principle is presented using the temperature–entropy diagram. This proof is simple and is independent of the proof of the first Carnot principle. The Carnot relation for thermal efficiency is also obtained simultaneously for all totally reversible heat engines between the same two reservoirs. The concept of reversibility in heat transfers and the role of environments in heat engine cycles will be further clarified and could be better understood using the proof presented here, which will be useful both for teaching and performing research in thermodynamics.

Isolated Quantum Heat Engine

We present a theoretical and numerical analysis of a quantum system that is capable of functioning as a heat engine. This system could be realized experimentally using cold bosonic atoms confined to a double well potential that is created by splitting a harmonic trap with a focused laser. The system shows thermalization, and can model a reversible heat engine cycle. This is the first demonstration of the operation of a heat engine with a finite quantum heat bath.

A thermodynamically general theory for convective vortices

Convective vortices are common features of atmospheres that absorb lower-entropy-energy at higher temperatures than they reject higher-entropy-energy to space. These vortices range from small to large-scale and play an important role in the vertical transport of heat, momentum, and tracer species. Thus, the development of theoretical models for convective vortices is important to our understanding of some of the basic features of planetary atmospheres. The heat engine framework is a useful tool for studying convective vortices. However, current theories assume that convective vortices are reversible heat engines. Since there are questions about how reversible real atmospheric heat engines are, their usefulness for studying real atmospheric vortices is somewhat controversial. In order to reduce this problem, a theory for convective vortices that includes irreversible processes is proposed. The paper's main result is that the proposed theory provides an expression for the pressure drop along streamlines that includes the effects of irreversible processes. It is shown that a simplified version of this expression is a generalization of Bernoulli's equation to convective circulations. It is speculated that the proposed theory not only explains the intensity, but also sheds light on other basic features of convective vortices such as their physical appearance.

A thermodynamically general theory for convective vortices

Convective vortices are common features of atmospheres that absorb lower-entropy-energy at higher temperatures than they reject higher-entropy-energy to space. These vortices range from small to large-scale and play an important role in the vertical transport of heat, momentum, and tracer species. Thus, the development of theoretical models for convective vortices is important to our understanding of some of the basic features of planetary atmospheres.The heat engine framework is a useful tool for studying convective vortices. However, current theories assume that convective vortices are reversible heat engines. Since there are questions about how reversible real atmospheric heat engines are, their usefulness for studying real atmospheric vortices is somewhat controversial. In order to reduce this problem, a theory for convective vortices that includes irreversible processes is proposed.The paper’s main result is that the proposed theory provides an expression for the pressure drop along streamlines that includes the effects of irreversible processes. It is shown that a simplified version of this expression is a generalization of Bernoulli’s equation to convective circulations. It is speculated that the proposed theory not only explains the intensity, but also sheds light on other basic features of convective vortices such as their physical appearance.

Performance optimization of a solar driven heat engine with finite-rate heat transfer

An optimal performance analysis for an equivalent Carnot-like cycle heat engine of a parabolic-trough direct-steam-generation solar driven Rankine cycle power plant at maximum power and maximum power density conditions is performed. Simultaneous radiation-convection and only radiation heat transfer mechanisms from solar concentrating collector, which is the high temperature thermal reservoir, are considered separately. Heat rejection to the low temperature thermal reservoir is assumed to be convection dominated. Irreversibilities are taken into account through the finite-rate heat transfer between the fixed temperature thermal reservoirs and the internally reversible heat engine. Comparisons proved that the performance of a solar driven Carnot-like heat engine at maximum power density conditions, which receives thermal energy by either radiation-convection or only radiation heat transfer mechanism and rejects its unavailable portion to surroundings by convective heat transfer through heat exchangers, has the characteristics of (1) a solar driven Carnot heat engine at maximum power conditions, having radiation heat transfer at high and convective heat transfer at low temperature heat exchangers respectively, as the allocation parameter takes small values, and of (2) a Carnot heat engine at maximum power density conditions, having convective heat transfer at both heat exchangers, as the allocation parameter takes large values. Comprehensive discussions on the effect of heat transfer mechanisms are provided.

The maser as a reversible heat engine

In a maser, a state selector sends excited molecules or atoms to a resonant cavity, while ground-level particles are not allowed to enter the resonator. The excited particles radiate their energy in the form of coherent electromagnetic oscillation. In this way the thermal energy of the atoms is transformed into useful work. Is this transformation equivalent to the Maxwell demon violating the second law? We explain the thermodynamics of an idealized maser system which works as a reversible heat engine and show how the second law reveals its validity during the conversion of heat into coherent radiation and mechanical work. We discuss different working regimes of the system. In particular, the ideal engine can either work with two heat reservoirs and convert heat into maser radiation with the Carnot efficiency, or, if working with a single heat reservoir, the engine can convert mechanical work entirely into maser radiation.

Facilitando a compreensão da segunda lei da termodinâmica

A idéia central desse artigo é chamar a atenção para o uso do diagrama T x s na descrição das máquinas térmicas reversíveis. Este diagrama mostra-se extremamente adequado e eficaz no ensino da segunda lei da tertermodinâmica dos processos reversíveis, no entanto uma escolha mostra-se mais apropriada que a outra quando se pretende salientar a universalidade dessa lei e não restringir a análise a uma substância de operação específica com é gás ideal.

Comments on “Frictional Dissipation in a Precipitating Atmosphere”

Abstract Pauluis et al. argue that frictional dissipation of energy around falling hydrometeors is an important entropy source in the tropical atmosphere. Their calculations suggest that the frictional dissipation around hydrometeors is about ⅓ of the work available from a reversible convective heat engine. Moreover, based on the residual of the energy budget of a numerical model, not shown in their note, the authors argue that irreversible entropy sources due to diffusion of water vapor and phase changes reduce the mechanical work available from the convective heat engine by about ⅔. Pauluis et al. conclude that only a tiny fraction of the energy potentially available from a convective heat engine is used to perform work. Renno and Ingersoll show that frictional heating can be easily included in the heat engine framework via increases in the thermodynamic efficiency of a reversible heat engine. It is shown that the effect of any other irreversible process is merely to reduce the thermodynamic efficiency ...

Clarifying reversible efficiency misconceptions of high temperature fuel cells in relation to reversible heat engines

High temperature fuel cells are promising energy conversion devices. Optimal design and analysis require a thorough understanding of their second law limitations. Fuel cells do not produce work from thermal energy as do heat engines. This has led to the provocative statement that fuel cells are ‘non-Carnot limited’. This label easily, yet erroneously, connotes that an ideal fuel cell is superior to an externally reversible heat engine. Clarity is achieved by analyzing the corresponding systems of these technologies. Conventional reversible fuel cell efficiency is also addressed, and a modified relation is developed. It accounts for the needed coupling of high temperature fuel cells with reversible heat engines, in order for maximum work to be produced.