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I'm reading a combustion text and would like help interpreting the following passage (diagram attached). It is regarding the relationship between equivalence ratio and adiabatic flame temperature:

For equivalence ratios between $\phi$ = 1 and $\phi$ ($T_{max}$), the heat capacity decrease more rapidly with $\phi$ than $\Delta H$, while beyond $\phi$ ($T_{max}$), $\Delta H$ falls more rapidly than does the heat capacity. The decrease in heat capacity is dominated by the decrease in the number of product moles formed per mole of fuel burned, with the decrease in the mean specific heat being less significant.

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I’m assuming that we are keeping the total mass of reactants constant (just changing the proportion between them). I get that total heat generated goes down since less fuel is reacting. But I don’t understand why heat capacity (I think this is extensive) decreases. Octane (at least at 300K ) has a higher specific heat than $\ce{CO2}$ and $\ce{H2O}$, so doesn’t having more fuel vapor increase the heat capacity?

For the last sentence, I don’t understand why a decrease in heat capacity is more significant than the decrease in mean specific heat?

The phrase “decrease in the number of product moles formed per mole of fuel burned,” does “mole of fuel burned” include fuel that technically didn’t react, since we have a fuel rich mixture?

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