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GATE ME 2021 Set 1 — Question 59

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NAT+2 / -0MediumZeroth & First LawsLaws & PropertiesThermodynamicsIdeal & Real Gas Behaviour

Thermodynamics → Laws & Properties → Ideal & Real Gas Behaviour

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Question

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 ∘C5\text{ }^\circ\text{C}, 105 kPa105\text{ kPa} with a volume flow rate of 1.25 m3/s1.25\text{ m}^3/\text{s} during steady state operation. Fresh air enters the mixing chamber at 34 ∘C34\text{ }^\circ\text{C} and 105 kPa105\text{ kPa}. The mass flow rate of the fresh air is 1.61.6 times of the cold air stream. Air leaves the room through the exit duct at 24 ∘C24\text{ }^\circ\text{C}.
Schematic of an air-conditioning system showing mixing of cold and fresh air before entering a room
Assuming the air behaves as an ideal gas with cp=1.005 kJ/kg.Kc_p = 1.005\text{ kJ/kg.K} and R=0.287 kJ/kg.KR = 0.287\text{ kJ/kg.K}, the rate of heat gain by the air from the room is ________ kW\text{kW} (round off to two decimal places).
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