Carnot Heat Engine Research Articles

Mechanical Efficiency of Photochromic Nanomotors, From First Principles.

Photochromic molecular motors hold promise for a multitude of potential applications in fields ranging from medicine to communications and structural repair. Yet, it is still a challenge to predict their mechanical efficiency. Here, azobenzene is explored as a representative light-driven nanomotor and estimate its quantum yield of photoisomerization and maximum mechanical efficiency. This is based on first-principles mapping of the 3D potential energy surfaces for the ground and excited states of the trans and cis configurations and identifying the minimum energy pathway for isomerization. A work cycle is devised and identifies force constant as the parameter that resembles temperature in the Carnot heat engine, but with very different efficiencies. The results show that the optomechanical efficiency of azobenzene at constant load is about 5% albeit under ideal conditions. To test the hypothesis, the study also explores the optomechanical efficiency of stilbene and 2-butene and shows that their efficiency does not exceed 5%.

Research on the application of heat engine efficiency in reducing energy consumption

In recent years, the problem of global warming and environmental pollution has become increasingly serious, so improving the efficiency of heat engines is of great significance to reduce energy consumption. This paper uses the method of literature review to study the current situation and prospects of heat engine efficiency in reducing energy consumption in three aspects. Firstly, the heat engine and its efficiency are summarized from the theoretical derivation. Secondly, the working principles of the Carnot heat engine and the Stirling heat engine are explained in detail through formula derivation and comparative analysis. Finally, taking the air-source heat pump as an example, we explain the basic principle, operation mechanism, and technical ways to improve efficiency in detail.

Carnot, Stirling, and Ericsson stochastic heat engines: Efficiency at maximum power.

This work uses the low-dissipation strategy to obtain efficiency at maximum power from a stochastic heat engine performing Carnot-, Stirling- and Ericsson-like cycles at finite time. The heat engine consists of a colloidal particle trapped by optical tweezers, in contact with two thermal baths at different temperatures, namely hot (T_{h}) and cold (T_{c}). The particle dynamics is characterized by a Langevin equationwith time-dependent control parameters bounded to a harmonic potential trap. In a low-dissipation approach, the equilibrium properties of the system are required, which in our case, can be calculated through a statelike equationfor the mean value 〈x^{2}〉_{eq} coming from a macroscopic expression associated with the Langevin equation.

Quantum heat engine with identical particles and level degeneracy

In this paper, the effects of identical particles and energy-level degeneracy on the work output of the quantum Otto and Stirling heat engines are studied. For quantum Otto heat engine, we find the effects of degeneracy in the ground state and in the excited state are same in the high-temperature limitation while the work done by a system with n-fold degeneracy in the excited state (ground state) is n ([Formula: see text]) times the one without degeneracy in the single-particle case. Moreover, the effects of the identical two-level systems with degeneracy in the ground state or excited state as working substances are discussed. The results of such problem for the Stirling and Carnot heat engines are similar. By analytical derivations in two limit conditions, we conclude that for the cycles which are composed of the quantum adiabatic process, isochoric process and isothermal process have similar results.

Rotating Lifshitz-like black holes in F(R) gravity

Abstract One of the alternative theories of gravitation with a possible UV completion of general relativity is Horava–Lifshitz gravity. Regarding a particular class of pure F(R) gravity in three dimensions, we obtain an analytical rotating Lifshitz-like black hole solution. We first investigate some geometrical properties of the obtained solution that reduces to a charged rotating Banados–Teitelboim–Zanelli black hole in a special limit. Then, we study the optical features of such a black hole, like the photon orbit and the energy emission rate, and discuss how electric charge, angular momentum, and exponents affect them. To have acceptable optical behavior, we should apply some constraints on the exponents. We continue our investigation by studying the thermodynamic behavior of solutions in the extended phase space and explore the validity of the first law of thermodynamics as well as local thermal stability using heat capacity. Evaluating the existence of van der Waals-like phase transition, we obtain critical quantities and show how they change under the variation of black hole parameters. Finally, we construct a holographic heat engine of such a black hole and obtain its efficiency in a cycle. Comparing the obtained results with the well-know Carnot heat engine efficiency, we examine the second law of thermodynamics.

Generalizing the isothermal efficiency by using Gaussian distributions.

Unlike the Carnot heat engine efficiency published in 1824, an isothermal efficiency derived from thermodynamics and information theory can be applied to biological systems. The original approach by Pierce and Cutler in 1959 to derive the isothermal efficiency equation came from Shannon's channel capacity of 1949 and from Felker's 1952 determination of the minimum energy dissipation needed to gain a bit. In 1991 and 2010 Schneider showed how the isothermal efficiency equation can be applied to molecular machines and that this can be used to explain why several molecular machines are 70% efficient. Surprisingly, some macroscopic biological systems, such as whole ecosystems, are also 70% efficient but it is hard to see how this could be explained by a thermodynamic and molecular theory. The thesis of this paper is that the isothermal efficiency can be derived without using thermodynamics by starting from a set of independent Gaussian distributions. This novel derivation generalizes the isothermal efficiency equation for use at all levels of biology, from molecules to ecosystems.

Minimum power consumption of multistage irreversible Carnot heat pumps with heat transfer law of q ∝ (ΔT) m

Abstract For the given initial finite high-temperature heat reservoir temperature, continuous Hamilton–Jacobi–Bellman equations are established to obtain optimal finite high-temperature heat reservoir temperature for minimum power consumption of multistage Carnot heat pumping system with generalized convective heat transfer law [q ∝ (ΔT) m ]. Analytical expression of optimal heat reservoir temperature with Newtonian heat transfer law (m = 1) is obtained based on generalized optimization results for minimum power consumption. For other heat transfer laws (m ≠ 1), numerical solutions for minimum power consumption are provided. Optimization results for multistage Carnot heat pumps are compared with maximum power output solutions of multistage irreversible Carnot heat engines.

2D or Not 2D: A Thermodynamic Approach to Modeling Space Solar Cells’ Efficiency with 2D Materials

Approximately 3 billion people have never used the internet due to its costs and inaccessibility, particularly in developing countries. To provide these areas with affordable internet, reducing the cost of building and launching satellites has become paramount in the assessment of their design, particularly their solar cells. While three-dimensional semiconductor materials like gallium arsenide (GaAs) have been the main material used in these cells to convert solar energy into electrical energy, two-dimensional (2D) materials like tellurene have demonstrated properties that warrant consideration. This research evaluates the potential of a novel 7-junction space solar cell configuration consisting of manganese phosphorus trisulfide, tungsten disulfide, rhenium disulfide, molybdenum disulfide, molybdenum ditelluride, bismuth oxyselenide, and tellurene to replace current 3-junction configurations using GaAs-based materials. Thermodynamic expressions, including the efficiency of a Carnot heat engine and a geometric optimization approach using the Shockley-Queisser triangle, were analyzed to derive equations for two properties critical to a space solar cell: efficiency and specific power. Computational simulations were run, and the results indicate that a 7-junction space solar cell configuration using 2D materials can enable a maximum efficiency gain of 12%, a mass reduction by over one-fifth, and a specific power output improvement of 54% at lower costs compared to GaAs-based space solar cells. The implications of this study point to the performance and cost feasibility of satellite usage for a broad range of applications, with social and environmental significance.

Assessment of the exergy and power density potential in the effluent flow of wastewater treatment plants

In this paper, historical data from the seven wastewater treatment plants in the Metropolitan Water Reclamation District of Greater Chicago (MWRDGC) is analyzed for its potential of waste heat recovery. The potential recovered waste heat is calculated monthly and yearly from effluent flow data and average regional minimum and maximum temperatures over a 10-year period between the years of 2011–2020. Based on the data analyzed, between 79.98 and 381.02 GWh/year could be recovered from all wastewater treatment plants in the MWRDGC combined. While the temperature differences between the effluent flow and the ambient temperature ranged between 0.3 and 19.2 °C, the primary factor in work energy potential was found to be the effluent mass flow rates, which ranged between 24,800 and 36,600 kg/s. Additionally, by viewing the work energy potential as the thermal source to either a theoretical Carnot heat engine or an endoreversible heat engine, a corresponding theoretical mechanical power output can be calculated. Despite Carnot and endoreversible thermal efficiencies of less than 5%, a power density between 0.004 and 2.84 W/m2 was calculated for every month except for June – August and was found to be comparable to hydropower generation systems.

Maximizing power output of endoreversible non-isothermal chemical engine via linear irreversible thermodynamics

Maximum power performance of an endoreversible non-isothermal chemical engine (NICE) with simultaneous heat and mass transfer is investigated in this paper. The heat and mass transfer processes are assumed to obey Onsager equations in linear irreversible thermodynamics. The power output of the endoreversible NICE as well as the corresponding vector efficiency [See Eq. (13) in this paper for its definition] are obtained analytically. Special cases for an endoreversible Carnot heat engine with the linear phenomenological heat transfer law [q∝Δ(T−1)] and an endoreversible isothermal chemical engine with the linear mass transfer law [g∝Δ(μ)] are further derived based on the general optimization results. Some numerical examples are provided, and the effects of changes of absorbed energy flux rate, mass flux rate, and heat and mass transfer phenomenological coefficients on the optimization results are analyzed. The results show that there are optimal absorbed energy flux rate and optimal mass flux rate for the power output of the endoreversible NICE to approach to its maximum; the relationship between the power output of the endoreversible NICE and its vector efficiency is paraboloid.

Performance analysis and optimization of an irreversible Carnot heat engine cycle for space power plant

In this paper, an irreversible Carnot heat engine cycle model for space power plants is built by using finite time thermodynamics. A radiator panel is considered between low temperature heat sink and space environment, expressions for power output and thermal efficiency of the plant are derived. Influences of internal irreversibility effect and thermal leakage loss on the optimal power output performance are analyzed when thermal conductivity of hot- and cold-sides heat exchangers are given. For the fixed total area of three heat exchangers the double-maximum power output and double-maximum thermal efficiency are obtained further by optimizing area distributions of hot- and cold- side heat exchangers and radiator, and by optimizing temperature of low-temperature heat sink. Influences of internal irreversibility effect and thermal leakage loss on the optimal performances are investigated. The results show that when taking power output as optimization objective, if considering thermal leakage and irreversibility effect, internal irreversibility effect increases from 1.1 to 1.3, double maximum power output decreases from 216.38 kW to 139.85 kW and decreases by 35.37%, the optimal the temperature the low-temperature heat sink decreases from 556K to 501.1K and decreases by 9.87%, and the optimal area allocations of hot- and cold-side heat exchangers decrease from 0.213 to 0.182 and decreases by 14.55%, from 0.213 to 0.207 and decreases by 2.82%, respectively, and that of radiator increases from 0.563 to 0.611 (an increase of 8.35%). Such temperature and area distribution condition ensure the future design of plant conversion system that aligns better performances and compactness.

Surface Gravity Wave Effect on Hurricane Energetics

Theoretical researches have established that the energy dynamics of a mature tropical cyclone may be idealized to be very similar to a theoretical Carnot heat engine. Assuming the dissipative heating of the atmospheric boundary layer and the net production of mechanical energy in the cyclone dominate the energy budget of the storm, the potential maximum wind speed of the cyclone can be approximated as a function of the air–sea temperature difference (Ts − T0) and specific enthalpy (k0*−k) difference: |Vmax|2≈CkCDTs−T0T0(k0*−k). Although this theory gives a straighforward estimate of maximum tropical cyclone intensity, studies found that few real storms achieve this theoretical maximum estimated using climatological atmospheric conditions and sea surface temperatures. The discrepancies were attributed to a lack of knowledge of the values of the drag coefficient (CD) and surface exchange coefficient for enthalpy (Ck), and on insufficient upper ocean thermal measurements under hurricanes. Recent observational and numerical studies have unearthed another possible factor for these discrepancies by showing that the energy flux into surface gravity waves under extreme wind conditions can be an order of magnitude greater than formerly believed, and thus may play an important role in the energy budget of tropical cyclones. In this study, numerical experiments are performed to investigate the effect of surface gravity waves under a range of idealized tropical cyclone winds. The wave fields are simulated using the WAVEWATCH III model. Our results demonstrate that by considering the energy flux to surface gravity waves, the potential maximum wind speed can be reduced by up to 12% and this ratio varies with the storm size, intensity, and translation speed.

Performance Analysis and Optimization for Irreversible Combined Carnot Heat Engine Working with Ideal Quantum Gases.

An irreversible combined Carnot cycle model using ideal quantum gases as a working medium was studied by using finite-time thermodynamics. The combined cycle consisted of two Carnot sub-cycles in a cascade mode. Considering thermal resistance, internal irreversibility, and heat leakage losses, the power output and thermal efficiency of the irreversible combined Carnot cycle were derived by utilizing the quantum gas state equation. The temperature effect of the working medium on power output and thermal efficiency is analyzed by numerical method, the optimal relationship between power output and thermal efficiency is solved by the Euler-Lagrange equation, and the effects of different working mediums on the optimal power and thermal efficiency performance are also focused. The results show that there is a set of working medium temperatures that makes the power output of the combined cycle be maximum. When there is no heat leakage loss in the combined cycle, all the characteristic curves of optimal power versus thermal efficiency are parabolic-like ones, and the internal irreversibility makes both power output and efficiency decrease. When there is heat leakage loss in the combined cycle, all the characteristic curves of optimal power versus thermal efficiency are loop-shaped ones, and the heat leakage loss only affects the thermal efficiency of the combined Carnot cycle. Comparing the power output of combined heat engines with four types of working mediums, the two-stage combined Carnot cycle using ideal Fermi-Bose gas as working medium obtains the highest power output.

Construction of a quantum Carnot heat engine cycle

The microscopic state description of an irreversible quantum Carnot cycle for a general quantum working medium is investigated. An efficiency lag term, which quantifies the deviation of the irreversible cycle efficiency from the classical Carnot efficiency, is given in terms of the total entropy increase in the universe. The efficiency lag and the total entropy increase in the universe are directly connected to the quantum relative entropy between the density matrices obtained at the end of the quantum adiabatic and the relaxation steps of the cycle. The total entropy increase and the efficiency lag are found to be always nonnegative quantities. Our results give a direct proof that the irreversible cycle efficiency is always smaller than the classical Carnot efficiency. Two interacting spins under an external magnetic field are proposed as the working medium of the irreversible quantum Carnot cycle. The external magnetic field is considered to be quasistatically changed during the steps of the cycle. The coupling between the spins is found to break down the scale invariance and make the quantum Carnot cycle irreversible. It is shown that while the quantum coupling can lower the cycle efficiency monotonically to zero, it can make the irreversible cycle to produce more work than the one obtained from the uncoupled spins. The conditions in which one can always construct a reversible Carnot cycle for the coupled spin working medium are also given.

Optimal Power and Efficiency of Multi-Stage Endoreversible Quantum Carnot Heat Engine with Harmonic Oscillators at the Classical Limit.

At the classical limit, a multi-stage, endoreversible Carnot cycle model of quantum heat engine (QHE) working with non-interacting harmonic oscillators systems is established in this paper. A simplified combined cycle, where all sub-cycles work at maximum power output (MPO), is analyzed under two types of combined form: constraint of cycle period or constraint of interstage heat current. The expressions of power and the corresponding efficiency under two types of combined constrains are derived. A general combined cycle, in which all sub-cycles run at arbitrary state, is further investigated under two types of combined constrains. By introducing the Lagrangian function, the MPO of two-stage combined QHE with different intermediate temperatures is obtained, utilizing numerical calculation. The results show that, for the simplified combined cycle, the total power decreases and heat exchange from hot reservoir increases under two types of constrains with the increasing number (N) of stages. The efficiency of the combined cycle decreases under the constraints of the cycle period, but keeps constant under the constraint of interstage heat current. For the general combined cycle, three operating modes, including single heat engine mode at low “temperature” (SM1), double heat engine mode (DM) and single heat engine mode at high “temperature” (SM2), appear as intermediate temperature varies. For the constraint of cycle period, the MPO is obtained at the junction of DM mode and SM2 mode. For the constraint of interstage heat current, the MPO keeps constant during DM mode, in which the two sub-cycles compensate each other.

Quantum-dot heat engines with irreversible heat transfer

This work establishes a quantum heat engine considering qubits as the external heat transfer mediums. The authors find that the efficiency and the power output of the quantum heat engine are closely dependent on the microproperties of qubits, and consequently relate the irreversible heat transfer with quantum effects. The equivalent conditions between the quantum heat engines and the classical endoreversible Carnot heat engines are revealed

P–v criticality and heat engine efficiency for Bardeen Einstein–Gauss–Bonnet AdS black hole

In this paper, we discuss the P–v criticality and the heat engine efficiency in the Bardeen Einstein–Gauss–Bonnet (EGB) AdS black hole space–time. From the P–v plane in the extended phase space, we find that the Bardeen EGB-AdS black hole conforms to Van der Waals (VdW) liquid–gas systems in the extended phase space, and of the Bardeen EGB-AdS black hole system is between 0.3333 of the Gauss–Bonnet AdS black hole system and 0.375 of the VdW gas system in the 5-dimensions. Then we construct a heat engine by taking the Bardeen EGB-AdS black hole as the working substance, and consider a rectangle heat cycle in the P–v plane. We find that two cases with different Bardeen parameter e and Gauss–Bonnet parameter α both have the same situation, i.e. as the entropy difference between small black hole S1 and large black hole S2 increases, the heat engine efficiency will increase. Furthermore, as the Bardeen parameter e increases, the efficiency will decrease. However, for the Gauss–Bonnet parameter α, the result is contrary. By comparing with the well-know Carnot heat engine efficiency, we have found the efficiency ratio η/ηc versus entropy S2 is bounded below 1, so it is coincided with the thermodynamical second law.

Power and efficiency optimization of an irreversible quantum Carnot heat engine working with harmonic oscillators

This paper takes a quantum heat engine model as research object. The heat engine works with harmonic oscillators. The engine cycle is an irreversible Carnot cycle which has four branches (two of them are isothermal branches and others are irreversible adiabatic branches). The adiabatic process is irreversible and heat leakage is also taken into account. This paper derives power and efficiency and provides numerical illustration. At high temperature limit, the optimal performance is also analysed with numerical illustrations, and influence of the irreversibility on the performance is analysed, too.

PERFORMANCE AND ECOLOGICAL OBJECTIVE INVESTIGATION OF TWO-STATE IRREVERSIBLE QUANTUM HEAT ENGINE

This paper considers irreversible two-state quantum Carnot heat engine. Basic thermodynamic parameters including power output and energy efficiency are considered, besides ecological function. Ecological function gives someone information about balance between power output and exergy destruction. The results show that ecological function have maximum (optimum) point for a and there is no optimum point for any parameter for x and y. All parameters are compared with each other and the most convenient operation conditions are recommended.

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».