Quantum dual engine based on a particle in a two-dimensional symmetrical potential well

A single particle-based quantum dual engine in a two-dimensional symmetrical potential well has been studied to determine its thermal efficiency formulation. This quantum efficiency of the engine will be compared to the classical version, the gas in the piston tube, which is considered still needs to be improved its efficiency according to the second law of thermodynamics. By analogizing the variables that exist in the classical system to the quantum system, heat energy and work for the five thermodynamic processes in a quantum dual cycle can be extracted. The main result is obtained that the thermal efficiency of a dual quantum engine has similar formulations with the classical counterpart. The higher heat capacity ratio of the quantum system has the effect of higher efficiency of the quantum dual engine than the efficiency of the classical version at the same compression ratio, cut-off ratio, and pressure ratio.