A. M. Tsirlin

Thermo-mechanical systems with several heat reservoirs: maximum power processes

Abstract While endoreversible heat-to-power conversion systems operating between two heat reservoirs have been intensely studied, systems with several reservoirs have attracted little attention. Here we analyse the maximum power processes of such systems with stationary temperature reservoirs. We find that independent of the number of reservoirs the working fluid uses only two isotherms and two infinitely fast isentropes/adiabats. One surprising result is that there may be reservoirs that are never used. This feature is explained for a simple system with three heat reservoirs.

Maximum power processes for multi-source endoreversible heat engines

The maximum power processes of multi-source endoreversible engines with stationary temperature reservoirs are investigated. We prove that the optimal solution is always time independent with a single hot and a cold engine contact temperature. The heat reservoirs fall into three groups: the hot reservoirs which are connected at all times for heat delivery, the cold reservoirs which are connected at all times for heat drain, and possibly a group of reservoirs at intermediate temperatures which are unused. This phenomenon is demonstrated for a three-source system. We find that for a commonly used class of heat transfer functions, including Newtonian, Fourier, and radiative heat transport, the efficiencies at maximum power are the same as for two-reservoir engines with appropriately chosen properties.

Irreversibility and Limiting Possibilities of Macrocontrolled Systems: II. Microeconomics

The methods of finite time thermodynamics are used to solve the maximal profit problem in irreversible microeconomic systems, similar to the problems of generalized exergy, which were solved in the first part of the paper. The condition of equilibrium in open microeconomic systems is obtained.

Optimal control of the parametric oscillator

We present a solution to the minimum time control problem for a classical harmonic oscillator to reach a target energy ET from a given initial state (qi ,p i) by controlling its frequency ω, ωmin ω ωmax. A brief synopsis of optimal control theory is included and the solution for the harmonic oscillator problem is used to illustrate the theory. (Some figures in this article are in colour only in the electronic version)

Evaluating the Efficiency Frontier of Separation Processes

The problem of finding the minimum work to be done to separate a mixture at a fixed process duration or at a given process capacity is considered. The estimates of the work done in an irreversible process substantially exceed those of the work done in reversible separation, and the work done in irreversible separation of depleted mixtures is finite even when the concentration of the minor component is arbitrarily close to zero. A method is proposed for extending these estimates to separation processes consuming heat rather than mechanical energy.

Consideration of irreversibility factors for binary distillation

Irreversibility factors affecting the energy consumption in the separation of a mixture in a binary distillation column are considered. The additional energy consumption related to fixed column productivity is estimated from below and compared with the consumption following from relations of equilibrium thermodynamics.

Optimal control in a quantum cooling problem

Abstract The optimal control for cooling a quantum harmonic oscillator by controlling its frequency is considered. It is shown that this singular problem may be transformed with the proper choice of coordinates to an equivalent problem which is no longer singular. The coordinates used are sufficiently simple that a graphical solution is possible and eliminates the need to use a Weierstrass-like approach to show optimality. The optimal control of this problem is of significance in connection with cooling physical systems to low temperatures. It is also mathematically significant in showing the power and limitations of coordinate transformations for attacking apparently singular problems.

Finite-time thermodynamics. Active potentiostatting

The paper addresses minimization of the dissipation in systems maintaining constant temperature or other constant intensive variables (potentiostatted systems). The entropy production and energy consumption of such systems are reduced from those of the traditional scheme if additional chambers are interposed between the system and its surroundings, in which intermediate values of thermodynamic potentials are maintained. The analysis is applied to a cryogenic system but it can be extended to high-temperature systems and to the systems in which insulation from mass transfer (constant chemical potential) or electrical conductivity (constant electrical potential) is maintained.

Finding limiting possibilities of thermodynamic systems by optimization

We consider typical problems of the field called the finite time thermodynamics (also called the optimization thermodynamics). We also outline selected formal methods applied to solve these problems and discuss some results obtained. It is shown that by introducing constraints imposed on the intensity of fluxes and on the magnitude of coefficients in kinetic equations, it is possible not only to investigate limiting possibilities of thermodynamic systems within the considered class of irreversible processes, but also to state and solve problems whose formulation has no meaning in the class of reversible processes. This article is part of the themed issue ‘Horizons of cybernetical physics’.

Optimal organization of binary distillation

The limiting potential of binary distillation is considered for conventional heat supply to the column bottom and heat removal from the refluxer and for heat supply and removal distributed over the column height. For either case, the limiting column capacity and the minimum heat consumption are related to the external stream compositions and to the heat and mass transfer coefficients.