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The efficiency at maximum power (EMP) of heat engines operating as generators is one corner stone of finite-time thermodynamics, the Curzon-Ahlborn efficiency ηCA being considered as a universal upper bound. Yet, no valid counterpart to ηCA has been derived for the efficiency at maximum cooling power (EMCP) for heat engines operating as refrigerators. In this Letter we analyse the reasons of the failure to obtain such a bound and we demonstrate that, despite the introduction of several optimisation criteria, the maximum cooling power condition should be considered as the genuine equivalent of maximum power condition in the finite-time thermodynamics frame. We then propose and discuss an analytic expression for the EMCP in the specific case of exoreversible refrigerators.

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International audienceA clay-based material exhibiting high pore volume fraction andlow thermal conductivity suitable for thermal insulation isdescribed. Starting with a commercial clay containing >75% kaolinite,foams were made by mixing in water and methyl celluloseas a surfactant then beating. After drying at 70°C, the pore volumefraction >94% remains almost constant for treatments upto 1150°C. In contrast, the phases constituting the solid skeletonevolve strongly with removal of surfactant, dehydroxylation ofkaolinite, and formation of mullite. The latter leads to greatermechanical strength but also an increase in thermal conductivity.Thermal treatment of the kaolin foam at 1100°C yields a suitablecompromise between low thermal conductivity of 0.054W.(m.K) – 1 at room temperature with a compressive yield stressof 0.04 MPa. The radiation component in the effective thermalconductivity is <10% at 20°C increasing to >50% at 500°

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