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## A Precise Formulation of the Third Law of Thermodynamics

Wreszinski, Walter Felipe; Abdalla, Elcio
Fonte: SPRINGER Publicador: SPRINGER
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
45.89%
The third law of thermodynamics is formulated precisely: all points of the state space of zero temperature I""(0) are physically adiabatically inaccessible from the state space of a simple system. In addition to implying the unattainability of absolute zero in finite time (or ""by a finite number of operations""), it admits as corollary, under a continuity assumption, that all points of I""(0) are adiabatically equivalent. We argue that the third law is universally valid for all macroscopic systems which obey the laws of quantum mechanics and/or quantum field theory. We also briefly discuss why a precise formulation of the third law for black holes remains an open problem.; CNPq; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); FAPESP ( Brazil)

## Finite-time thermodynamics: Engine performance improved by optimized piston motion

Mozurkewich, Michael; Berry, R. S.
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Publicado em /04/1981 EN
Relevância na Pesquisa
65.9%
The methods of finite-time thermodynamics are used to find the optimal time path of an Otto cycle with friction and heat leakage. Optimality is defined by maximization of the work per cycle; the system is constrained to operate at a fixed frequency, so the maximum power is obtained. The result is an improvement of about 10% in the effectiveness (second-law efficiency) of a conventional near-sinusoidal engine.

## Optimal paths for minimizing lost available work during heat transfer processes with a generalized heat transfer law

Xia,Shaojun; Chen,Lingen; Sun,Fengrui
Fonte: Sociedade Brasileira de Física Publicador: Sociedade Brasileira de Física
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/03/2009 EN
Relevância na Pesquisa
55.76%
A common of finite-time heat transfer processes between high- and low-temperature sides with a generalized heat transfer law [q ∝ (Δ(Tn ))m] are studied in this paper. The optimal heating and cooling configurations for minimizing lost available work are derived for the fixed initial and final temperatures of the working fluid of the system (low-temperature side). Optimal paths are compared with the common strategies of constant heat flux, constant source (reservoir) temperature and the minimum entropy generation operation by numerical examples. The condition corresponding to the minimum lost available work strategy is that corresponding to a constant rate of lost available work, not only valid for Newton's heat transfer law [q ∝ ΔT] but also valid for the generalized convective heat transfer law [q ∝ (ΔT)m ]. The obtained results are more general and can provide some theoretical guidelines for the designs and operations of practical heat exchangers.

## Finite-time thermodynamics of port-Hamiltonian systems

Delvenne, Jean-Charles; Sandberg, Henrik
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.97%
In this paper, we identify a class of time-varying port-Hamiltonian systems that is suitable for studying problems at the intersection of statistical mechanics and control of physical systems. Those port-Hamiltonian systems are able to modify their internal structure as well as their interconnection with the environment over time. The framework allows us to prove the First and Second laws of thermodynamics, but also lets us apply results from optimal and stochastic control theory to physical systems. In particular, we show how to use linear control theory to optimally extract work from a single heat source over a finite time interval in the manner of Maxwell's demon. Furthermore, the optimal controller is a time-varying port-Hamiltonian system, which can be physically implemented as a variable linear capacitor and transformer. We also use the theory to design a heat engine operating between two heat sources in finite-time Carnot-like cycles of maximum power, and we compare those two heat engines.; Comment: To appear in Physica D (accepted July 2013)

## Reconstruction of $f(T)$ gravity: Rip cosmology, finite-time future singularities and thermodynamics

Bamba, Kazuharu; Myrzakulov, Ratbay; Nojiri, Shin'ichi; Odintsov, Sergei D.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.07%
We demonstrate that there appear finite-time future singularities in $f(T)$ gravity with $T$ being the torsion scalar. We reconstruct a model of $f(T)$ gravity with realizing the finite-time future singularities. In addition, it is explicitly shown that a power-low type correction term $T^\beta$ ($\beta>1$) such as a $T^2$ term can remove the finite-time future singularities in $f(T)$ gravity. Moreover, we study $f(T)$ models with realizing inflation in the early universe, the $\Lambda$CDM model, Little Rip cosmology and Pseudo-Rip cosmology. It is demonstrated that the disintegration of bound structures for Little Rip and Pseudo-Rip cosmologies occurs in the same way as in gravity with corresponding dark energy fluid. We also discuss that the time-dependent matter instability in the star collapse can occur in $f(T)$ gravity. Furthermore, we explore thermodynamics in $f(T)$ gravity and illustrate that the second law of thermodynamics can be satisfied around the finite-time future singularities for the universe with the temperature inside the horizon being the same as that of the apparent horizon.; Comment: 38 pages, no figure, version accepted for publication in Physical Review D

## Near-equilibrium universality and bounds on efficiency in quasi-static regime with finite source and sink

Johal, Ramandeep S.; Rai, Renuka
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.87%
We show the validity of some results of finite-time thermodynamics, also within the quasi-static framework of classical thermodynamics. First, we consider the efficiency at maximum work (EMW) from finite source and sink modelled as identical thermodynamic systems. The near-equilibrium regime is characterized by expanding the internal energy upto second order (i.e. upto linear response) in the difference of initial entropies of the source and the sink. It is shown that the efficiency is given by a universal expression $2 \eta_C / (4-\eta_C)$, where $\eta_C$ is the Carnot efficiency. Then, different sizes of source and sink are treated, by combining different numbers of copies of the same thermodynamic system. The efficiency of this process is found to be ${\boldsymbol\eta}_0 = \eta_C/ (2-\gamma \eta_C)$, where the parameter $\gamma$ depends only on the relative size of the source and the sink. This implies that within the linear response theory, EMW is bounded as ${\eta_C}/{2} \le {{\boldsymbol\eta}}_0 \le {\eta_C}/{(2 - \eta_C)}$, where the upper (lower) bound is obtained with a sink much larger (smaller) in size than the source. We also remark on the behavior of the efficiency beyond linear response.; Comment: 11 pages, no figures. New discussion added on universality beyond linear response

## Weighted reciprocal of temperature, weighted thermal flux, and their applications in finite-time thermodynamics

Sheng, Shiqi; Tu, Z. C.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
65.94%
The concepts of weighted reciprocal of temperature and weighted thermal flux are proposed for a heat engine operating between two heat baths and outputting mechanical work. With the aid of these two concepts, the generalized thermodynamic fluxes and forces can be expressed in a consistent way within the framework of irreversible thermodynamics. Then the efficiency at maximum power output for a heat engine, one of key topics in finite-time thermodynamics, is investigated on the basis of a generic model under the tight-coupling condition. The corresponding results have the same forms as those of low-dissipation heat engines [M. Esposito, R. Kawai, K. Lindenberg, and C. Van den Broeck, {Phys. Rev. Lett.} \textbf{105}, 150603 (2010)]. The mappings from two kinds of typical heat engines, such as the low-dissipation heat engine and the Feynman ratchet, into the present generic model are constructed. The universal efficiency at maximum power output up to the quadratic order is found to be valid for a heat engine coupled symmetrically and tightly with two baths. The concepts of weighted reciprocal of temperature and weighted thermal flux are also transplanted to the optimization of refrigerators.; Comment: 13 journal pages, 2 figures

## Quantum Thermodynamics

Kosloff, Ronnie
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.9%
Quantum thermodynamics addresses the emergence of thermodynamical laws from quantum mechanics. The link is based on the intimate connection of quantum thermodynamics with the theory of open quantum systems. Quantum mechanics inserts dynamics into thermodynamics giving a sound foundation to finite-time-thermodynamics. The emergence of the 0-law I-law II-law and III-law of thermodynamics from quantum considerations is presented. The emphasis is on consistence between the two theories which address the same subject from different foundations. We claim that inconsistency is the result of faulty analysis pointing to flaws in approximations.

## Finite time thermodynamics for a single level quantum dot

Esposito, Massimiliano; Kawai, Ryoichi; Lindenberg, Katja; Broeck, Christian Van den
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
65.94%
We investigate the finite time thermodynamics of a single-level fermion system interacting with a thermal reservoir through a tunneling junction. The optimal protocol to extract the maximum work from the system when moving the single energy level between an initial higher value and a final lower value in a finite time is calculated from a quantum master equation. The calculation also yields the optimal protocol to raise the energy level with the expenditure of the least amount of work on the system. The optimal protocol displays discontinuous jumps at the initial and final times.; Comment: 7 pages, 5 figures

## Thermodynamic optimization of a Penrose process: an engineers' approach to black hole thermodynamics

Bravetti, Alessandro; Gruber, Christine; Lopez-Monsalvo, Cesar S.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.04%
In this work we present a new view on the thermodynamics of black holes introducing effects of irreversibility by employing thermodynamic optimization and finite-time thermodynamics. These questions are of importance both in physics and in engineering, combining standard thermodynamics with optimal control theory in order to find optimal protocols and bounds for realistic processes without assuming anything about the microphysics involved. We find general bounds on the maximum work and the efficiency of thermodynamic processes involving black holes that can be derived exclusively from the knowledge of thermodynamic relations at equilibrium. Since these new bounds consider the finite duration of the processes, they are more realistic and stringent than their reversible counterparts. To illustrate our arguments, we consider in detail the thermodynamic optimization of a Penrose process, i.e. the problem of finding the least dissipative process extracting all the angular momentum from a Kerr black hole in finite time. We discuss the relevance of our results for real astrophysical phenomena, for the comparison with laboratory black holes analogues and for other theoretical aspects of black hole thermodynamics.; Comment: 12 pages, 4 figures. Comments are welcome!

## Continuity and boundary conditions in thermodynamics: From Carnot's efficiency to efficiencies at maximum power

Ouerdane, Henni; Apertet, Yann; Goupil, Christophe; Lecoeur, Philippe
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.06%
[...] By the beginning of the 20th century, the principles of thermodynamics were summarized into the so-called four laws, which were, as it turns out, definitive negative answers to the doomed quests for perpetual motion machines. As a matter of fact, one result of Sadi Carnot's work was precisely that the heat-to-work conversion process is fundamentally limited; as such, it is considered as a first version of the second law of thermodynamics. Although it was derived from Carnot's unrealistic model, the upper bound on the thermodynamic conversion efficiency, known as the Carnot efficiency, became a paradigm as the next target after the failure of the perpetual motion ideal. In the 1950's, Jacques Yvon published a conference paper containing the necessary ingredients for a new class of models, and even a formula, not so different from that of Carnot's efficiency, which later would become the new efficiency reference. Yvon's first analysis [...] went fairly unnoticed for twenty years, until Frank Curzon and Boye Ahlborn published their pedagogical paper about the effect of finite heat transfer on output power limitation and their derivation of the efficiency at maximum power, now known as the Curzon-Ahlborn (CA) efficiency. The notion of finite rate explicitly introduced time in thermodynamics...

## Optimal ratios of the piston speeds for a finite speed endoreversible Carnot heat engine cycle

Feng,Huijun; Chen,Lingen; Sun,Fengrui
Fonte: Sociedad Mexicana de Física Publicador: Sociedad Mexicana de Física
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/04/2010 EN
Relevância na Pesquisa
75.99%
The performance of an endoreversible Carnot heat engine cycle is analyzed and optimized using the theory of finite time thermodynamics based on Agrawal and Menon's i model of finite speed of the piston on the four branches and Curzon and Ahlborn's ii model of finite rate of heat transfer. The finite speeds of the piston on the four branches are further assumed to be different, which is unlike the model of constant-speed of the piston on the four branches. The analytical formula between power and efficiency of the cycle is derived for a fixed cycle period. There exist optimal ratios of the finite piston speeds on the four branches. The effects of the temperature ratio of the heat reservoirs on the dimensionless power versus efficiency of the cycle and isothermal expansion ratio are obtained by numerical examples.

## Maximum efficiency of an irreversible heat engine with a distributed working fluid and linear phenomenological heat transfer law

Chen,Lingen; Xia,Shaojun; Sun,Fengrui
Fonte: Sociedad Mexicana de Física Publicador: Sociedad Mexicana de Física
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/06/2010 EN
Relevância na Pesquisa
65.87%
Maximum efficiency of an irreversible heat engine with a distributed working fluid, in which the heat transfers between the working fluid and the heat reservoirs obey the linear phenomenological heat transfer law , is studied in this paper by using finite-time thermodynamics based on Orlov and Berry's work i. Two kinds of efficiencies are defined, and the problems are divided into three cases. Optimal control theory is used to determine the upper bounds of efficiencies of the heat engines for various cases. Numerical examples of the two efficiencies for the irreversible heat engine with lumped-parameter model working between variable temperature reservoirs are provided, and the effects of changes of the reservoir's temperature on the maximum efficiency of the heat engine are analyzed. The obtained results are also compared with those obtained by Orlov and Berry ii with Newtonian heat transfer law .

## Finite-time exergy with a finite heat reservoir and generalized radiative heat transfer law

Xia,Shaojun; Chen,Lingen; Sun,Fengrui
Fonte: Sociedad Mexicana de Física Publicador: Sociedad Mexicana de Física
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/08/2010 EN
Relevância na Pesquisa
75.95%
The problem of the maximum work that can be extracted from a system consisting of one finite heat reservoir and one subsystem with the generalized radiative heat transfer law [q ∞ Δ (Tn)] is investigated in this paper. Finite-time exergy is derived for a fixed duration and a given initial state of the subsystem by applying optimal control theory. The optimal subsystem temperature configuration for the finite-time exergy consists of three segments, including the initial and final instantaneous adiabatic branches and the intermediate heat transfer branch. Analyses for special examples show that the optimal configuration of the heat transfer branch with Newton's heat transfer law [q ∞ Δ (T)] is that the temperatures of the reservoir and the subsystem change exponentially with time and the temperature ratio between them is a constant; The optimal configuration of the heat transfer branch with the linear phenomenological heat transfer law [q ∞ Δ (T-1)] is such that the temperatures of the reservoir and the subsystem change linearly and non-linearly with time, respectively, and the difference in reciprocal temperature between them is a constant. The optimal configuration of the heat transfer branch with the radiative heat transfer law [q ∞ Δ (T4)] is significantly different from those with the former two different heat transfer laws. Numerical examples are given...

## Exergoeconomic performance optimization for an endoreversible regenerative gas turbine closed-cycle cogeneration plant

Tao,Guisheng; Chen,Lingen; Sun,Fengrui
Fonte: Sociedad Mexicana de Física Publicador: Sociedad Mexicana de Física
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/06/2009 EN
Relevância na Pesquisa
55.76%
Finite time exergoeconomic performance of an endoreversible regenerative gas turbine closed-cycle cogeneration plant coupled to constant temperature heat reservoirs is investigated. The analytical formulae about profit rate and exergy efficiency of the cogeneration plant with the heat resistance losses in the hot-, cold- and consumer-side heat exchangers and the regenerator are deduced, respectively. By means of numerical calculations, the heat conductance allocation among the four heat exchangers and pressure ratio of the compressor are optimized by taking the maximum profit rate as the objective. The characteristic of optimal dimensionless profit rate versus corresponding exergy efficiency is investigated and the effects of design parameters on optimal performance of the cogeneration plant are also analyzed. The results show that there exist a sole group of optimal heat conductance allocations among the four heat exchangers and an optimal pressure ratio of the compressor which lead to the maximum dimensionless profit rate, and there exists an optimal consumer-side temperature which leads to double-maximum dimensionless profit rate.

## Finite-time thermoeconomic optimization of a non endoreversible heat engine model

Barranco-Jiménez,M.A.
Fonte: Sociedad Mexicana de Física Publicador: Sociedad Mexicana de Física
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/06/2009 EN
Relevância na Pesquisa
55.76%
Within the context of Finite-Time Thermodynamics (FTT), we study the thermoeconomics of a simplified non-endoreversible thermal power plant model (the so-called Novikov engine). In our study, we use different heat transfer laws: the so called Newton's law of cooling, the Stefan-Boltzmann radiation law, the Dulong-Petit's law and another phenomenological heat transfer law. We use two FTT optimization criteria: the maximum power regime (MP) and the so-named modified ecological criterion for performance analysis. This last criterion leads the engine model towards a mode of performance that appreciably diminishes the engine's wasted energy. It is shown that under ecological conditions the plant dramatically reduces the amount of heat rejected to the environment, and a loss of profit is translated into a better usage of fuel such that the heat rejected towards the environment is remarkably reduced compared to that of a maximum power regime. Besides, we analyze the effect on the reduction of power output and the optimal efficiencies in terms of an internal irreversibility parameter that comes from the Clausius inequality which characterizes the degree of internal irreversibility.

## Effect of heat transfer on the performance of a thermoelectric heat pump driven by a thermoelectric generator

Chen,Lingen; Meng,Fankai; Sun,Fengrui
Fonte: Sociedad Mexicana de Física Publicador: Sociedad Mexicana de Física
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/08/2009 EN
Relevância na Pesquisa
65.97%
A model of a thermoelectric heat pump driven by a thermoelectric generator with external heat transfer irreversibility is proposed. The performance of the combined thermoelectric heat pump device obeying Newton's heat transfer law is analyzed using the combination of finite time thermodynamics and non-equilibrium thermodynamics. Two analytical formulae for heating load versus working electrical current, and the coefficient of performance (COP) versus working electrical current, are derived. For a fixed total heat transfer surface area of four heat exchangers, the allocations of the heat transfer surface area among the four heat exchangers are optimized for maximizing the heating load and the COP of the combined thermoelectric heat pump device. For a fixed total number of thermoelectric elements, the ratio of the number of thermoelectric elements of the generator to the total number of thermoelectric elements is also optimized for maximizing both the heating load and the COP of the combined thermoelectric heat pump device. The influences of thermoelectric element allocation and heat transfer area allocation are analyzed by detailed numerical examples. The optimum working electrical currents for maximum heating load and maximum COP at different total numbers of thermoelectric elements and different total heat transfer areas are provided...

## Heating load, COP, exergy loss rate, exergy output rate and ecological optimizations for a class of generalized irreversible universal heat pump cycles

Chen,Lingen; Feng,Huijun; Sun,Fengrui
Fonte: Sociedad Mexicana de Física Publicador: Sociedad Mexicana de Física
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/08/2010 EN
Relevância na Pesquisa
65.87%
The optimal performance of a class of generalized irreversible universal steady flow heat pump cycle model, which consists of two heat-absorbing branches, two heat-releasing branches and two irreversible adiabatic branches with the losses of heat-resistance, heat leakage and internal irreversibility is analyzed by using finite time thermodynamics. The analytical formulae about heating load, coefficient of performance (COP), exergy loss rate, exergy output rate and ecological function of the universal heat pump cycle are derived. Moreover, performance comparisons among maximum COP condition, a given exergy output rate condition and maximum ecological function condition are carried out by using numerical examples. It is shown that the ecological function objective is an excellent candidate objective with the ideal of an ecological and long-term goal. The effects of heat leakage and internal irreversibility on the cycle performance are discussed. The universal cycle model gives a unified description of seven heat pump cycles, and the results obtained include the performance characteristics of Brayton, Otto, Diesel, Atkinson, Dual, Miller and Carnot heat pump cycles with the losses of heat-resistance, heat leakage and internal irreversibility.

## On the optimum operation conditions of an endoreversible heat engine with different heat transfer laws in the thermal couplings

Barranco-Jiménez,M.A.; Sánchez-Salas,N.; Angulo-Brown,F.
Fonte: Sociedad Mexicana de Física Publicador: Sociedad Mexicana de Física
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/08/2008 EN
Relevância na Pesquisa
65.87%
Within the context of Finite-Time Thermodynamics (FTT) we study the optimum operating conditions of an endoreversible engine model. In this model we consider different heat transfer modes from the hot reservoir to the working fluid, while the mode of heat transfer from the working fluid to the cold reservoir is governed by a Newtonian heat transfer law. In our analysis we use two modes of performance, the maximum power regimen and the so-called ecological function. We calculate the optimum temperatures of the working fluid and the optimum efficiency in terms of the relevant system parameters. We show how the efficiency under a maximum ecological function is greater than the maximum efficiency under maximum power conditions.

## Optimization of an irreversible Carnot engine in finite time and finite size

Aragón-González,G.; Canales-Palma,A.; León-Galicia,A.; Morales-Gómez,J.R.
Fonte: Sociedad Mexicana de Física Publicador: Sociedad Mexicana de Física
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/08/2006 EN
Relevância na Pesquisa
65.93%
In this work, we consider the class of irreversible Carnot engines that results from combining the characteristics of two models found in the literature: the model in finite time and the model in finite size. The performance of the resulting model, including three irreversibilities, was doubly-optimized in finite time and finite size. The first optimization of power and efficiency, maintaining the thermal conductances fixed, was performed in finite time. Since the optimum time ratio from the first optimization, is the same for both maximum power and maximum efficiency, this means that the model can be newly optimized but now in finite size. Then, the second optimization, maintaining the overall heat transfer coefficient constant, was performed. For both optimizations, analytical expressions for the efficiency that maximizes the power and maximum efficiency were obtained. Changing the order in which partial optimizations were carried out, a remarkable optimal property was obtained: the resources of total contact time and the total area of heat transfer are proportional.