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The efficiency at maximum power (EMP) of irreversible Carnot-like heatengines is investigated based on the weak endoreversible assumption and thephenomenologically irreversible thermodynamics. It is found that the weakendoreversible assumption can reduce to the conventional one for the heatengines working at maximum power. Carnot-like heat engines are classified intothree types (linear, superlinear, and sublinear) according to differentcharacteristics of constitutive relations between the heat transfer rate andthe thermodynamic force. The EMPs of Carnot-like heat engines are proved to bebounded between $\eta_C/2$ and $\eta_C/(2-\eta_C)$ for the linear type, 0 and$\eta_C/(2-\eta_C)$ for the superlinear type, and $\eta_C/2$ and $\eta_C$ forthe sublinear type, respectively, where $\eta_C$ is the Carnot efficiency.

Bounds of efficiency at maximum power for linear, superlinear and sublinear irreversible Carnot-like heat engines