Methane $($CH$4)$ at $298$K$,1$ atm enters a furnace operating at steady state and burns completely with $140\%$ of theoretical air entering at $400$K$,1$ atm. The products of combustion exit at $500$K$,1$atm. The flow rate of the methane is $1$ kg$/$min$.$ Kinetic and potential energy effects are negligible and air can be modeled as $21\%$ O$2$ and $79\%$ N$2$ on a molar basis.$$ Determine the dew point temperature of the products, in K