In case of a single stage compression refrigeration system operating between constant evaporator and condenser temperatures, the maximum possible COP is given by Carnot COP:

If we assume that heat rejection at the absorber and condenser takes place at same external heat sink temperature To, then a vapour absorption refrigeration system operates between three temperature levels, Tg, To and Te. The maximum possible COP of a refrigeration system operating between three temperature levels can be obtained by applying first and second laws of thermodynamics to the system.

Figure above shows the various energy transfers and the corresponding temperatures in an absorption refrigeration system.

From first law of thermodynamics, where Qe is the heat transferred to the absorption system at evaporator temperature Te, Qg is the heat transferred to the generator of the absorption system at temperature Tg, Qa+c is the heat transferred from the absorber and condenser of the absorption system at temperature To and Wp is the work input to the solution pump.

From second law of thermodynamics, where ΔStotal is the total entropy change which is equal to the sum of entropy change of the system ΔSsys and entropy change of the surroundings ΔSsurr. Since the refrigeration system operates in a closed cycle, the entropy change of the working fluid of the system undergoing the cycle is zero, i.e., ΔSsys = 0 . The entropy change of the surroundings is given by:

Substituting the expression for first law of thermodynamics in the above equation

Neglecting solution pump work, Wp; the COP of VARS is given by:

An ideal vapour absorption refrigeration system is totally reversible (i.e., both internally and externally reversible). For a completely reversible system the total entropy change (system+surroundings) is zero according to second law, hence for an ideal VARS:

Hence

Hence combining first and second laws and neglecting pump work, the maximum possible COP of an ideal VARS system is given by:

Thus the ideal COP is only a function of operating temperatures similar to Carnot system. It can be seen from the above expression that the ideal COP of VARS system is equal to the product of efficiency of a Carnot heat engine operating between Tg and To and COP of a Carnot refrigeration system operating between To and Te, i.e.,

Thus an ideal vapour absorption refrigeration system can be considered to be a combined system consisting of a Carnot heat engine and a Carnot refrigerator as shown here:

Thus the COP of an ideal VARS increases as generator temperature (Tg) and evaporator temperature (Te) increase and heat rejection temperature (To) decreases. However, the COP of actual VARS will be much less than that of an ideal VARS due to various internal and external irreversibilities present in actual systems.