Efficiency of a Carnot engine at maximum power output

Abstract

The efficiency of a Carnot engine is treated for the case where the power output is limited by the rates of heat transfer to and from the working substance. It is shown that the efficiency, η, at maximum power output is given by the expression η = 1 − (T2/T1)1/2 where T1 and T2 are the respective temperatures of the heat source and heat sink. It is also shown that the efficiency of existing engines is well described by the above result.

From Thermal Rectifiers to Thermoelectric Devices

“…In the limit ZT → ∞, η(P max ) takes its maximum value of η C /2. Such value also corresponds to the linear response expansion of the so-called Curzon-Ahlborn upper bound [155,39,108,45,143,129,59,5]. Therefore, high values of ZT are favorable for thermoelectric conversion.…”

Principles of control thermodynamics

“…Thus we take what most texts would call a quasistatic process of a simple system and ask what the constraint of a given time might mean for such a process. 8 Our first result concerns something we choose to call Principle 0 (Callen [14]): If we are given infinite time, we can make the quasistatic process of our simple system reversible.…”

“…While the approach of Berry and co-workers [4][5][6][7] and of Curzon and Ahlborn [8] treated reciprocating operation of heat engines, the approach of Bejan [2,9] was based on steady-state operation of a distributed cycle. The difference in focus between these two approaches implies a real physical difference in the way the processes are conceptualized.…”

Maximum power, ecological function and efficiency of an irreversible Carnot cycle: a cost and effectiveness optimization

“…Thus, the thermal efficiency given in equation (1.1) does not have great significance and is a poor guide for the performances of real heat engines. A more realistic upper bound could be placed on the efficiency of a heat engine operating at its maximum power point; the so-called CA efficiency (Curzon-Alhborn [1]):…”