Consider operation of the furnace-re-cooperator combination of problem under conditions for which chemical energy is converted to thermal energy in the combustor at a rate of q _comb = 2.0 x 10⁶ Wand energy is transferred from the combustion gases to the load in the furnace at a rate of q _load = 1.4 X 10⁶ W. Assuming equivalent flow rates (m_c = m_h = 1.0 kg/s) and specific heats (c_p,c = c_p,h = 1200 J/kg ∙K) for the cold air and flue gases in the re-cooperator, determine T_h,i, T_h,o, and T_c,o when T_c,i = 300 K and the re-cooperator has an effectiveness of ε = 0.30. What value of the effectiveness would be needed to achieve a combustor air inlet temperature of 800 K?