  We formulate the work output and efficiency for linear irreversible heat
engines working between a finite-sized hot heat source and an infinite-sized
cold heat reservoir until the total system reaches the final thermal
equilibrium state with a uniform temperature. We prove that when the heat
engines operate at the maximum power under the tight-coupling condition without
heat leakage the work output is just half of the exergy, which is known as the
maximum available work extracted from a heat source. As a consequence, the
corresponding efficiency is also half of its quasistatic counterpart.
