Efficiencies of power plants, quasi-static models and the geometric-mean temperature

Abstract

Observed efficiencies of industrial power plants are often approximated by the square-root formula: $1-\sqrt{T_{-}/T_{+}}$, where $T_{+}(T_{-})$ is the highest (lowest) temperature achieved in the plant. This expression can be derived within finite-time thermodynamics, or, by entropy generation minimization, based on finite rates of processes. A closely related quantity is the optimal value of the intermediate temperature for the hot stream, which is given by the geometric-mean value: $\sqrt{T_{+}{T}_{-}}$. It is proposed to model the operation of plants by quasi-static work extraction models, with one reservoir (source/sink) as finite, while the other as practically infinite. No simplifying assumption is made on the nature of the finite system. This description is consistent with two model hypotheses, each yielding a specific value of the intermediate temperature. We show that the expected value of the intermediate temperature, defined as the arithmetic mean, is very closely given by the geometric-mean value. The definition is motivated as the use of inductive inference in the presence of limited information.

Latex2e, 13 pages, five figures

References in corpus (5)

• H. B. Reitlinger and the origins of the Efficiency at Maximum Power formula for Heat Engines
• Work Output and Efficiency at Maximum Power of Linear Irreversible Heat Engines Operating with a Finite-Sized Heat Source
• Near-equilibrium universality and bounds on efficiency in quasi-static regime with finite source and sink
• Optimal performance of heat engines with a finite source or sink and inequalities between means
• Estimating performance of Feynman's ratchet with limited information

Cited by in corpus (5)

• Low-dissipation Carnot-like heat engines at maximum efficient power
• Global linear-irreversible principle for optimization in finite-time thermodynamics
• Efficiency at the maximum power of the power law dissipative Carnot-like Heat engines with non-adiabatic dissipation
• The many avatars of Curzon-Ahlborn efficiency
• Heat engine model exhibit super-universal feature and capture the efficiencies of different power plants