The total work produced by the turbine.
The total heat transferred to the air in the tank during the discharge.
Answer to Problem 200RP
The total work produced by the turbine is
The total heat transferred to the air in the tank during the discharge 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
Express the mass at any time.
Differentiate Equation (III) with respect to temperature.
Since the compressor operates as an isentropic device, express the temperature at state 4.
Here, temperature at state 3 is
Express the conservation of mass applied to the tank.
Here, change of mass is
Calculate the total power produced by the turbine after applied the first law.
Here, specific enthalpy at state 3 and 4 is
Substitute
Integrate Equation (V).
Calculate the total heat transferred to the air in the tank during the discharge.
Here, mass at initial and final state is
Conclusion:
Substitute 1 atm for
Substitute 10 atm for
Substitute
Thus, the total work produced by the turbine is
Substitute
Thus, the total heat transferred to the air in the tank during the discharge is
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Chapter 7 Solutions
Thermodynamics: An Engineering Approach
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