$2.(30$pts$)$ Consider the ideal cycle examples from homework $2.$ The fuel$/$air mixture is compressed from its initial state $($state $1)$ to TDC $($state $2).$ Combustion then proceeds to state $3$ in either a constant volume or constant pressure process. HW$2$ assumed constant specific heats. Test the validity of this assumption by calculating the percent error between the result from HW$2($table$)$ and calculated adiabatic flame temperatures for:

a$.(15$pts$)$ Constant volume combustion of iso$-$octane initially at state $2.$

b$.(15$ pts $)$ Constant pressure combustion of iso$-$octane initially at state $2.$