Air at T = 20C and P = 100 kPa enters a compressor with a mass...

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Air at T₁ = 20°C and P₁ = 100 kPa enters a compressor with a mass flow rate of m= 0.025 kg/s through a circular inlet pipe having an inner diameter of D₁ =1 cm. The compressor operates at steady state. The mechanical power input to the compressor is W = 3.5 kW. Air exits the compressor at T₂ = 50°C and P₂ = 650 kPa. The diameter of the exit pipe is large and therefore the velocity of the air leaving the compressor is small and its kinetic energy negligible. However, the kinetic energy of the air entering the compressor is not negligible. The outlet of the compressor is connected to a rigid storage tank having a volume of Vtank = 1.5 m³. The tank initially contains air at Pini 100 kPa. The pressure of the air within the tank rises as it is filled, but heat transfer between the tank and the surroundings keeps the temperature of the air in the tank always at Ttank = 25°C. This compressor is not adiabatic. Assume that the air obeys the ideal law with R = 287 J/kg-K. Assume that the specific heat capacities of air are constant and equal to cv = 717 J/kg-K and cp = 1005 J/kg-K. State and justify any other assumptions that you employ. a) Determine the velocity of the air entering the compressor (m/s). = b) Determine the rate of heat transfer to the compressor (W). c) Determine the mass of air in the tank after t = 200 sec of operation. d) Determine the pressure of the air in the tank after 200 sec of operation. e) Determine the total heat transfer from the tank to the room during 200 sec of operation. Air at T₁ = 20°C and P₁ = 100 kPa enters a compressor with a mass flow rate of m= 0.025 kg/s through a circular inlet pipe having an inner diameter of D₁ =1 cm. The compressor operates at steady state. The mechanical power input to the compressor is W = 3.5 kW. Air exits the compressor at T₂ = 50°C and P₂ = 650 kPa. The diameter of the exit pipe is large and therefore the velocity of the air leaving the compressor is small and its kinetic energy negligible. However, the kinetic energy of the air entering the compressor is not negligible. The outlet of the compressor is connected to a rigid storage tank having a volume of Vtank = 1.5 m³. The tank initially contains air at Pini 100 kPa. The pressure of the air within the tank rises as it is filled, but heat transfer between the tank and the surroundings keeps the temperature of the air in the tank always at Ttank = 25°C. This compressor is not adiabatic. Assume that the air obeys the ideal law with R = 287 J/kg-K. Assume that the specific heat capacities of air are constant and equal to cv = 717 J/kg-K and cp = 1005 J/kg-K. State and justify any other assumptions that you employ. a) Determine the velocity of the air entering the compressor (m/s). = b) Determine the rate of heat transfer to the compressor (W). c) Determine the mass of air in the tank after t = 200 sec of operation. d) Determine the pressure of the air in the tank after 200 sec of operation. e) Determine the total heat transfer from the tank to the room during 200 sec of operation.

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