
Concept explainers
The change in the work potential of the air stored in the tank.
The change in exergy of the air stored in the tank.

Answer to Problem 122RP
The change in the work potential of the air stored in the tank is
The change in exergy of the air stored in the tank is
Explanation of Solution
Write the formula to calculate initial mass of air in the tank
Here, initial pressure of air is
Write the formula to calculate final mass of air in the tank
Here, final pressure of air is
Write the formula to calculate temperature of air at state 2 using isentropic relation
Here, temperature of air at state 1 is
Apply the conservation of mass to the tank which gives the following relation.
Here, rate of change in mass of air is
Write the equation for the rate of heat transfer using the first law of thermodynamics
Here, enthalpy of air is h, internal energy of air is u, volume of tank is V, specific heat capacities at constant pressure and constant volume are
From the final temperature equation and multiplying the above relation by
Integrate the above relation.
Apply the first law to the tank and compressor.
Here, rate of work potential of the air stored in the tank is
Integrate the above relation.
Here, change in the work potential of the air stored in the tank is
Apply the first law and second law to the tank and compressor and the mass balance incorporated. It gives,
Here, dead state temperature is
Integrate the above relation.
Here, reversible work done on the system is
Conclusion:
Refer Table A-2, "Ideal-gas specific heats of various common gases", obtain the properties of air at the room temperature.
Substitute
Substitute
Substitute
Substitute
The negative sign shows that the work is done on the compressor.
Thus, the change in the work potential of the air stored in the tank is
Substitute
This is the exergy change of the air stored in the tank.
Thus, the change in exergy of the air stored in the tank is
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