Connection between maximum-work and maximum-power thermal cycles

Abstract

We propose a new connection between maximum-power Curzon-Ahlborn thermal cycles and maximum-work reversible cycles. This linkage is built through a mapping between the exponents of a class of heat transfer laws and the exponents of a family of heat capacities depending on temperature. This connection leads to the recovery of known results and to a wide and interesting set of new results for a class of thermal cycles. Among other results we find that it is possible to use analytically closed expressions for maximum-work efficiencies to calculate good approaches to maximum-power efficiencies.PACS numbers: 05.70.Ln Non-equilibrium and irreversible thermodynamics; 05.70.-a Thermodynamics; 84.60.Bk Performance characteristics of energy conversion systems, figure of merit.As it is well known, in 1975 [1] Curzon-Ahlborn (CA) found that an endoreversible Carnot-like thermal engine in which the isothermal branches of the cycle are not in thermal equilibrium with their corresponding heat reservoirs at absolute temperatures T 1 and T 2 < T 1 has an efficiency at the maximum-power (MP) regime given byThis equation was obtained by using the so-called Newton law of cooling to model the heat exchanges between the heat reservoirs and the working fluid along the isothermal branches of the cycle. In fact, Eq. (1) The square root term (SRT) observed in the CA-efficiency can be found in other processes of energy conversion, such as the so-called water powered machine, which mixes two steady streams of hot and cold water to produce an output stream of warm water at maximum kinetic energy [16]. In fact, the role of the SRT of temperatures is more general and it appears also in some irreversible processes such as the irreversible cooling or heating of an ideal gas initially at temperature T i in contact with a series of auxiliary reservoirs to reach the final temperature T f of a main heat reservoir, the SRT appears when the generation of entropy of this process is minimized [17]. As it can be seen, the SRT is found in several thermal processes (reversible or irreversible) subject to some extremal conditions. A result less known is that corresponding to the way the square root is lost in the case of reversible cycles operating at MW regime. In 1989 [14], LL first studied a cycle formed by two adiabatic processes and two paths with constant heat capacities C > 0 of the working fluid (see Fig. 1). This reversible cycle operating under MW conditions has an efficiency given by η CA = 1 − √ τ , where τ = T − /T + is the ratio between the minimum and maximum temperatures of the cycle (see Fig. 1). Actually, the first author in finding this expression for a MW engine was Chambadal [18]. LL [14] generalized the model of Fig. 1, to encompass a family of symmetric and asymmetric reversible cycles which have a MW efficiency that do no deviate from η CA more than 14%. This behavior was referred to as a near universality property of η CA . However, for the case of reversible cycles performing at MW, we will demonstrate that the CA-effici...

Heat devices in nonlinear irreversible thermodynamics

“…FTT focuses on irreversibilities caused by finite-rate heat transfers between the working fluid, and the external heat reservoirs, internal dissipation of the working fluid and heat leaks between the heat reservoirs. The optimization procedure in FTT, carried out under a fixed cycle time, usually assumes two degrees of freedom, that is, the inner temperatures of the isothermal steps of the working system [2,[4][5][6][7]. In spite of their analytical simplicity, these models * Present address: Department of Complex Systems Science, Graduate School of Information Science, Nagoya University, Nagoya 464-8601, Japan can reproduce, at least qualitatively, the power-efficiency and the cooling power-COP behaviors observed in real HE [6] and RE [8,9].…”

“…In spite of their analytical simplicity, these models * Present address: Department of Complex Systems Science, Graduate School of Information Science, Nagoya University, Nagoya 464-8601, Japan can reproduce, at least qualitatively, the power-efficiency and the cooling power-COP behaviors observed in real HE [6] and RE [8,9]. More simplified FTT models assume the so-called endoreversible approximation [2,4,[6][7][8], where the heat leaks and the internal dissipations are neglected. In this case, if the linear heat transfer laws are additionally assumed for the external heat exchange, the resulting efficiency at maximum power becomes the well-known Curzon-Ahlborn (CA) efficiency η CA = 1 − √ τ = 1 − √ 1 − η C [10].…”

Carnot-Like Heat Engines Versus Low-Dissipation Models

“…and depends on the values σ hc , τ and the exponent of the heat transfer law k as showed in [9]. In Figure 4a, η P max is depicted for the limiting cases σ hc → {0, ∞}.…”

Performance of micro two-level heat devices with prior information

“…It lay the foundation for finite time thermodynamics. Many revisions of the CA model have been made to describe the real-life heat engines more accurately, and some good results at the maximum power output criterion have been obtained [3][4][5][6][7]. Furthermore, the low dissipation model [8][9][10][11] and linear and minimally nonlinear irreversible heat engine models described by the Onsager relations and the extended Onsager relations [12][13][14] have been also proposed to study the efficiency and its bounds at MP criterion.…”