Fundamental optimal relation of an irreversible quantum Carnot heat pump with spin-1/2 systems

A model of an irreversible quantum heat pump with working medium consisting of many non-interacting spin-1/2 systems is established in this paper. The quantum heat pump cycle is composed of two isothermal processes and two irreversible adiabatic processes and is referred to as a spin quantum Carnot heat pump. Irreversibilities of heat resistance, internal friction and heat leakage are considered in this model. Using the quantum master equation, semi-group approach and finite time thermodynamics (FTT), this paper derives expressions of cycle period, heating load and coefficient of performance (COP) of the spin quantum Carnot heat pump. The fundamental optimal relation of the spin quantum heat pump at high temperature limit is deduced and analyzed using numerical examples. Effects of internal friction and heat leakage on the optimal performance of the spin quantum heat pump are discussed in detail. The endoreversible case, frictionless case and the case without heat leakage are discussed in brief.