Carnot-COP for sorption heat pumps working between four temperature levels

The theoretical efficiency limits of heat driven heat pumps operating between three and four temperatures are derived from the fundamental thermodynamical laws, i.e. the energy balance and the entropy balance. While in the three temperatures case the system is fully determined by specification of the three temperatures and the cooling capacity, a four temperature heat pump needs, in addition to the four temperatures and the cooling capacity, specification of an additional operating parameter. This can be, for example, the ratio of the two heat flows which are released at the two different intermediate temperatures. Various assumptions regarding this proportion are discussed with respect to their relevance for both the combination power cycle/vapor compression cycle as well as for single-effect sorption cycles. The present analysis shows that a single-effect sorption heat pump is principally not able to operate reversibly in an environment of four externally specified temperatures unless the four temperatures follow, incidentally, a correlation that is given by the equilibrium properties of the employed working fluids. Therefore, in endo-reversible models for four-temperature sorption cycles only three rather than four operating temperatures may be specified independently.