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To improve the coefficient of performance (COP) of CO 2 transcritical reverse cycle and determine the most efficient cycle, comparison analysis on single- and two-stage CO 2 transcritical cycles with internal heat exchanger (IHX) or expander is presented adopting the principle of thermodynamics. Results indicate that the COP of four cycles,namely single-stage compression with IHX (SI), single-stage compression with expander (SE), two-stage compression with IHX (TI) and two-stage compression with expander (TE), can be ranged as TE>SE>TI>SI. It presents that adopting an expander to recover expansion power is the primary method to improve the COP of CO 2 transcritical reverse cycle if the efficiency of the expander is up to a certain value. Under supposed operating condition, where the outlet temperature of gas cooler is 35 ℃ and the evaporating temperature is 5 ℃, the COP of TE cycle is about 42% higher than that of SI cycle when the expander efficiency is 0.6 and the degree of superheat of IHX is 15 ℃. Therefore TE cycle is the most recommendatory one and it is better to adopt TE in those high-cooling capacity systems because its technology cost will be higher.