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We develop a general method for calculating the thermal efficiency ofarbitrary thermodynamic cycles defined in the pressure-volume ($p-V$) diagram.To demonstrate how effective our approach is, we calculate the thermalefficiency of ideal gas engines for a few non-trivial cycles in the $p-V$diagram, including a circular shape, a heart shape, a cycloid of Ceva, and astar-shaped curve. We determine the segments along the cycle where heat isabsorbed or released from the heat engine. Our method can be applied to any gasmodel, and, as an example, we present the results for the van der Waals gas.

General formalism for calculating the thermal efficiency of thermodynamic cycles defined in a $p-V$ diagram