At approximately atmospheric pressure, methane gas is burned completely with 30% excess air. Both the air and methane enter the furnace at 30 °C saturated with water vapor, and the flue gases leave the furnace at 1500 °C. Calculate how much heat is lost from the furnace per mole of methane. In your solution, show analytically all calculations, including the analytical derivation of the number of moles of water vapor entering the furnace. Use steam tables to determine Psat, and compare your answer with the answer you would obtain using Antoine’s and Wagner’s equations. For the latter, you can determine A, B, C, D as in ** above.