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Engine efficiency at maximum power, entropy production and equilibrium thermodynamics

The Carnot engine sets an upper limit to the efficiency of a practical heat engine. An arbitrary irreversible engine is sometimes believed to behave closely as the Curzon-Ahlborn engine. Efficiency of the latter is obtained commonly by invoking the maximum power principle in a non-equilibrium framework. We outline here two plausible routes within the domain of classical thermodynamics to arrive at the same expression. Further studies on the performances of available practical engines reveal that a simpler approximate formula works much better in respect of bounds to the efficiency. Putting an intermediate-temperature reservoir between the actual source and the sink leads to a few interesting extra observations.