Consider an isothermal and isobaric combustion system that operates as follows: a stream of fuel and air originally at T₀ and p₀ absorbs thermal energy reversibly from a regenerator reaching temperature T. It then enters a combustion chamber at temperature T and pressure p₀, where the fuel is combusted yielding enthalpy of combustion |?H_c(T)| per mole. This energy drives a reversible heat engine with T₊ = T and T_? = T₀. The combustion products leave the combustion chamber at temperature T and cool to temperature T₀ transferring some of their energy to the regenerator used to heat the incoming fuel?air stream. Assume that the (molar) heat capacity of the products exceeds the heat capacity of the reactants ( f (t) = C?_products(t) ? C?_reactants(t) > 0 for all t between T₀ and T), so some residual energy in the products can also be used to run a reversible heat engine as the products cool. Assume also that |?H_c(T₀)| > |?G_c(T₀)|, where ?G_c(T) is the Gibbs free energy of combustion. Show that the energy(maximum useful work) of the fuel combusted in this system is given by

Since ?G_c(T) must be negative for the combustion reaction to occur, B(T) reaches its maximum at T_M?where ?G_c(T_M) = 0.

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B(T) = -AG.(To) + AG.(T)