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

TL;DR

This paper explores the efficiency of power plants using quasi-static models and geometric mean temperatures, showing that the optimal intermediate temperature closely aligns with the arithmetic mean, based on limited information inference.

Contribution

It introduces a quasi-static modeling approach with finite and infinite reservoirs, linking efficiency formulas to geometric mean temperatures without simplifying assumptions.

Findings

The geometric mean temperature closely approximates the optimal intermediate temperature.

The efficiency formula aligns with finite-time thermodynamics and entropy minimization.

The arithmetic mean of the temperature is well approximated by the geometric mean.

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.