Concept explainers
The exergy destruction associate with the process.
Answer to Problem 81P
The exergy destruction associate with the process is
Explanation of Solution
Write formula for enthalpy departure factor
Here, the enthalpy at ideal gas state is
Rearrange the Equation (I) to obtain
Refer Equation (II) express as two states of enthalpy difference (final – initial).
Consider the propane as the real gas and the express the equation of state.
Here, the compressibility factor is
Here the compressibility factor is,
Rewrite the Equation (IV) as follows.
Consider the term
The internal energy is expressed as follows.
Here, the enthalpy is
Write the formula for change in internal energy.
While compression the boundary work is done on the system (piston-cylinder).
Write the formula for boundary work input.
Here, the negative sign indicates the work done on the system.
Write the energy balance equation for the system (piston-cylinder).
Here, the net energy in is
Refer Table A-1, “Molar mass, gas constant, and critical-point properties”.
The critical temperature and pressure of propane gas is as follows.
The gas constant
The specific heat at constant pressure
It is given that the propane is compressed isothermally. At ideal gas state the enthalpy is solely depends on temperature. Since, the process is isothermal (temperature is constant). Hence the change in enthalpy at ideal gas state becomes zero.
The reduced pressure
The reduced pressure
Write the entropy balance equation for closed system.
Here, the entropy input is
Rewrite the Equation (VII) as follows by substituting 0 for
Here, mass flow rate is
Write the formula for change in entropy
Here, the gas constant is R, the specific heat at constant pressure is
Write the formula for change in entropy
Here, the entropy departure factor is
Write the formula for exergy destruction associate with process.
Substitute
At initial:
Refer Figure A-29, “Generalized enthalpy departure chart”.
The enthalpy departure factor
Refer Figure A-30, “Generalized entropy departure chart”.
The entropy departure factor
Refer Figure A-15, “Nelson–Obert generalized compressibility chart”.
The compressibility factor
At final:
Refer Figure A-29, “Generalized enthalpy departure chart”.
The enthalpy departure factor
Refer Figure A-30, “Generalized entropy departure chart”.
The entropy departure factor
Refer Figure A-15, “Nelson–Obert generalized compressibility chart”.
The compressibility factor
Conclusion:
The average compressibility factor is,
Substitute
Substitute
Substitute
Substitute
Here, the negative sign indicates the heat is transferred out from the system.
Substitute
Substitute
Substitute
Thus, the exergy destruction associate with the process is
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Chapter 12 Solutions
Thermodynamics: An Engineering Approach
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