GATE 2021 ME (ME1) – Question 59
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).
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Correct answer: 4.94 to 4.98
Explanation
Cold mass flow is $\dot m_c=P\dot V/(RT)=105(1.25)/(0.287\times278.15)=1.64414$ kg/s. Fresh flow is 1.6 times this, and mixed temperature is (5+1.6×34)/2.6=22.8462°C.
Room heat gain is $2.6\dot m_cc_p(24-22.8462)=\mathbf{4.96}$ kW. Celsius differences equal kelvin differences.