Estimate the maximum amount of work that can be obtained from the controlled combustion of methane in air at 1 bar as a function of the methane-to-air ratio. Assume that the process is as follows. First the methane is burned adiabatically so that the adiabatic flame temperature is obtained. Next a Carnot cycle is used to extract heat from the combustion products until they are cooled to 25°C. Note that the work cannot all be extracted from the combustion gases at the adiabatic flame temperature, but rather is extracted over a range of temperatures starting at the adiabatic flame temperature and ending at 25°C.