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We formulate the work output and efficiency for linear irreversible heatengines working between a finite-sized hot heat source and an infinite-sizedcold heat reservoir until the total system reaches the final thermalequilibrium state with a uniform temperature. We prove that when the heatengines operate at the maximum power under the tight-coupling condition withoutheat leakage the work output is just half of the exergy, which is known as themaximum available work extracted from a heat source. As a consequence, thecorresponding efficiency is also half of its quasistatic counterpart.

Work Output and Efficiency at Maximum Power of Linear Irreversible Heat Engines Operating with a Finite-Sized Heat Source