$[35$ points$]$ Methane at $25C$ is burned in a boiler furnace with $10\mathrm{.}0\%$ excess air preheated to $100C.$ Ninety percent of the methane fed is consumed, the product gas contains $10\mathrm{.}0$molC$\frac{O_2}{m}$olCO, and the combustion products leave the furnace at $400Cq,$ a$)$ Calculate the heat transferred from the furnace, $),$ for a basis of $1200mo\frac{l}{m}inC{H}_4$ fed. $($The greater the value of $Q,$ the more steam, is produced in the boiler.$)$

b$)$ Would the following changes increase or decrease the rate of steam production? $($Assume the fuel feed rate and fractional conversion of methane remain constant.$)$ Briefly explain your answers. $($i$)$ Increasing the temperature of the inlet air; $($ Increasing the percent excess air for a given stack gas temperature; $($iii$)$ Increasing the selectivity of $C{O}_2$ to CO formation in the furnace; $($iv$)$ Increasing the stack gas temperature.