the work output W is the "noble" energy stored in the hydrogen and oxygen products (e.g. released as electricity during fuel consumption in a fuel cell). It thus corresponds to the free Gibbs energy change of water-splitting ΔG, and is maximum according to Eq.(3) at the lowest temperature of the process (T°) where it is equal to ΔG°. the heat input Q is the heat provided by the hot source at temperature TH to the i endothermic reactions of the thermochemical cycle (the fuel consumption subsystem is exothermic): (12) Hence, each heat requirement at temperature TH is, (13) Replacing Eq.(13) in Eq.(12) yields: (14) Consequently, replacing W (ΔG°) and Q (Eq.(14)) in Eq.(11) gives after reorganization Eq.(10) (assuming that the ΔSi do not change significantly with the temperature, i.e. are equal to ΔS°i) Equation (10) has practical implications about the minimum number of reactions for such a process according to the maximum process temperature TH. Indeed, a numerical application (ΔG° equals to 229 kJ/K for water considered as steam) in the case of the originally chosen conditions (high-temperature nuclear reactor with TH and T° respectively equal to 1000K and 298K) gives a minimum value around 330 J/mol/K for the summation of the positive entropy changes ΔS°i of the process reactions. This last value is very high as most of the reactions have entropy change values below 50 J/mol/K, and even an elevated one (e.g. water-splitting from liquid water: 163 J/mol/K) is twice lower. Consequently, thermochemical cycles composed of less than three steps are practically impossible with the originally planned heat sources (below 1000K), or require "hybrid" versions Hybrid thermochemical cycles In this case, an extra freedom degree is added via a relatively small work input Wadd (maximum work consumption, Eq.(9) with ΔG ≤ Wadd), and Eq.(10) becomes, (15) If Wadd is expressed as a fraction f of the process heat Q (Eq.(14)), Eq.(15) becomes after reorganization, (16) Using a work input equals to a fraction f of the heat input is equivalent relative to the choice of the reactions to operate a pure similar thermochemical cycle but with a hot source with a temperature increased by the same proportion f. Naturally, this decreases the heat-to-work efficiency in the same proportion f. Consequently, if one want a process similar to a thermochemical cycle operating with a 2000K heat source (instead of 1000K), the maximum heat-to-work efficiency is twice lower. As real