The total work required to fill the tank.
The total heat transferred from the air in the tank.
Answer to Problem 199RP
The total work required to fill the tank is
The total heat transferred from the air in the tank is
Explanation of Solution
Refer to Table A-2Ea, obtain the properties of air at room temperature.
Calculate the initial mass of air in the tank.
Here, pressure and temperature at initial state is
Calculate the final mass of air in the tank.
Here, pressure and temperature at final state is
Since the compressor operates as an isentropic device, express the temperature at state 2.
Here, specific heat ratio is k.
Express the conservation of mass applied to the tank.
Here, change of mass is
Write the equation of total power required to fill the tank using first law.
Here, specific enthalpy at state 2 is
Merge the ideal gas equation of state and constant specific heats in Equation (III).
Use the temperature relation across the compressor and multiply by dt in Equation (IV).
Here, change in pressure is dP.
Integrate Equation (V) for initial and final states.
Here, pressures at initial and final states are
Apply the first law to the tank and compressor.
Here, specific enthalpy at initial state is
Integrate Equation (VII) to calculate the total heat transferred from the air in the tank.
Here, specific internal energy at initial and final state is
Conclusion:
Substitute 1 atm for
Substitute 10 atm for
Substitute
Thus, the total work required to fill the tank is
Substitute
Thus, the total heat transferred from the air in the tank is
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