
The second law efficiency and the exergy destruction during the expansion process.

Answer to Problem 97RP
The second law efficiency is
The exergy destruction during the expansion process is
Explanation of Solution
Write the expression to obtain the mole number of
Here, molar mass of
Write the expression to obtain the mole number of
Here, molar mass of
Write the expression to obtain the mole number of
Here, molar mass of
Write the expression to obtain the mole number of
Here, molar mass of
Write the expression to obtain the equation to calculate the mole number of the mixture
Write the expression to obtain the molar mass of the gas mixture
Write the expression to obtain the equation to calculate the constant-pressure specific heat of the mixture
Here, mass fraction of
Write the expression to obtain the gas constant of the mixture
Here, the universal gas constant is
Write the expression to obtain the constant volume specific heat
Write the expression to obtain the specific heat ratio
Write the expression to obtain the temperature at the end of the expansion for the isentropic process
Write the expression to obtain the actual outlet temperature
Here, efficiency of the turbine is
Write the expression to obtain the entropy change of the gas mixture
Write the expression to obtain the actual work output
Write the expression to obtain the reversible work output
Write the expression to obtain the second law efficiency
Write the expression to obtain the exergy destruction
Conclusion:
Refer Table A-1E, “Molar mass, gas constant, and critical point properties”, obtain the molar masses of
Substitute 0.15 lbm for
Substitute 0.5 lbm for
Substitute 0.6 lbm for
Substitute 0.2 lbm for
Substitute
Substitute 1 lbm for
Refer Table A-2Ea, “Ideal gas specific heats of various common gases”, obtain the constant pressure specific heats of
Substitute 0.15 for
Substitute
Substitute
Substitute
Substitute 1.323 for k,
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the second law efficiency is
Substitute
Thus, the exergy destruction during the expansion process is
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Chapter 13 Solutions
Thermodynamics: An Engineering Approach
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