A $13-m^3$ steel tank with mass of $1200kg$ is sealed and contains air at $100$kPa and $295K.$ The outer surface of the tank is perfectly insulated. The tank wall, however, exchanges heat with the gas in the tank so rapidly both are always at the same temperature. The tank is connected, through some piping with a valve $($closed initially$),$ to a compressed air line that has a steady and continuous flow at $500$kPa and $303$K$.$ The valve is then opened, and it remains open until $1000$ moles of air enter the tank. Find the temperature of the air in the tank when the filling process is completed. Take air to be an ideal gas with $C_p=3\mathrm{.}5R$ and $C_v=2\mathrm{.}5R,$ where $R$ is the gas constant. Take the specific heat of steel to be $448Jk{g}^{-1}{K}^{-1}.($ANS: $300K)$