GATE Mechanical Engineering (ME) 2021 Shift 1 Solved Paper

An air-conditioning system provides a continuous flow of air to a room using an intake duct and an exit duct, as shown in the figure. To maintain the quality of the indoor air, the intake duct supplies a mixture of fresh air with a cold air stream. The two streams are mixed in an insulated mixing chamber located upstream of the intake duct. Cold air enters the mixing chamber at 5°C, 105 kPa with a volume flow rate of 1.25 m3/s during steady state operation. Fresh air enters the mixing chamber at 34°C and 105 kPa. The mass flow rate of the fresh air is 1.6 times of the cold air stream. Air leaves the room through the exit duct at 24°C.

Assuming the air behaves as an ideal gas with c_p = 1.005 kJ/kg.K and R = 0.287 kJ/kg.K. the rate of heat gain by the air from the room is _______ kw (round off to two decimal places).