Methane burns in air by the following chemical reaction: This reaction can be idealized as a constant pressure or a constant volume process. Calculate the maximum temperatures of combustion for these two cases. Assume that the specific heats are constant for the temperature range of interest (use the value at 1500 K). Also assume that methane reacts with a stoichiometric amount of air and that the methane and air are initially at 500C and 10 atm. The heat of combustion at 25C for one kg of methane burned (lower heat value) is -50,010 kJ. (Note that no enthalpy of formation is given for the reactants and products in this problem.)

\begin{tabular}{lcc} \hline & Formula & cp(J/g/K) \\ methane & CH4 & 3.075 at 298773K \\ Oxygen & O2 & 0.983 at 298773K \\ Nitrogen & N2 & 1.078 at 298773K \\ water (vapor) & H2O & 2.617 at 1500K \\ nitrogen & N2 & 1.245 at 1500K \\ carbon dioxide & CO2 & 1.327 at 1500K \\ \hline \end{tabular}