This paper discusses the thermodynamics of a new air conditioning, refrigeration and heat pump cycle that embodies two heat transfer processes coupled with both a compression and an expansion process. The working medium of the new cycle is multicomponent in nature and, in general, consists of a superheated gaseous carrier component, such as air, in partnership with a phase-changing component, such as water. The basic cycle is described along with variations in system configuration. Simple analytical models and methods are introduced and applied to calculate cycle efficiencies for sample systems. It is shown that the reverse Brayton and reverse Rankine cycles are subcases of the new cycle. As well, the reverse Carnot can be approximated by this cycle. Further, it is shown that this new cycle yields ideal coefficients of performance (COP) greater than the reverse Brayton and reverse Rankine cycles. For example, in an "icemaking" heat pump configuration, with a source temperature of 32°F (O°C) and a maximum rejection temperature of 105°F (40.6°C), the ideal heating COP is 9.72 compared to an ideal COP for the R22 reverse Rankine cycle which is 7.25. In the air conditioning configuration, with a maximum condensing temperature of "150°F (65.6°C) and a minimum evaporation temperature of 40°F (4.4°C) the ideal cooling COP is 8.19 compared with an ideal R-12 vapor compression cycle COP of 4.26.