The endothermic decomposition of natural gas into a carbon-rich condensed phase and a hydrogen-rich gas phase, using concentrated solar energy as the source of high-temperature process heat, is considered as a model reaction for conducting a 2nd-law analysis of a solar decarbonization process in which carbon is removed from fossil fuels prior to their use for power generation. The theoretical maximum closed-cycle exergy efficiency, defined as the ratio of the Gibbs free energy change of the reaction to the solar power input, can be as high as 35% for a black-body solar cavity-receiver/reactor operating at 1500 K and under a mean solar flux concentration ratio of 1000, and decreases to 21% if the products exiting the solar reactor are quenched without recovering their sensible heat. Four technically viable routes are examined for extracting power from the chemical products of the solar decomposition of CH4: (1) carbon is sequestered and only H-2 is used in a fuel cell; (2) carbon is used to fuel a conventional Rankine cycle and H-2 is used in a fuel cell; (3) carbon is steam-gasified to syngas in a solar gasification process and the syngas further processed to H-2, which, together with H-2 from the CH4-decomposition reaction, is used in a fuel cell; and (4) carbon serves as a reducing agent of ZnO in a solar carbothermic process for producing Zn and CO that are further converted via water-splitting and water-shifting reactions to H-2 for use in a fuel cell, The open-cycle energy efficiency, defined as the ratio of electric power output to the thermal energy input (solar + heating value of reactants), exceeds 65% for the 3rd and 4th power generation routes. Both of these routes offer a net gain of 40% in the electrical output and, consequently, an equal percent reduction in the corresponding Specific CO2 emissions, vis-A-vis the direct use of CH4 for fueling a 55%-efficient combined Brayton-Rankine cycle. For route nr. 1, the energy penalty for avoiding CO2 emissions amounts to 30% of the electrical output.