Concept explainers
n-Octane [C8H18(l)] is burned in the constant-pressure combustor of an aircraft engine with 70 percent excess air. Air enters this combustor at 600 kPa and 327°C, liquid fuel is injected at 25°C, and the products of combustion leave at 600 kPa and 1227°C. Determine the entropy generation and exergy destruction per unit mass of fuel during this combustion process. Take T0 = 25°C.
(a)
The entropy generation from the combustion chamber per unit mass of fuel.
Answer to Problem 92P
The entropy generation from the combustion chamber per unit mass of fuel is
Explanation of Solution
Write the energy balance equation using steady-flow equation.
Here, the total energy entering the system is
Substitute
Here, the enthalpy of formation for product is
Calculate the molar mass of the
Here, the number of carbon atoms is
Write the expression for entropy generation during this process.
Write the combustion equation of Equation (IV)
Here, the entropy of the product is
Determine the entropy at the partial pressure of the components.
Here, the partial pressure is
Write the expression for exergy destruction during this process.
Here, the thermodynamic temperature of the surrounding is
Determine the entropy generation per unit mass of the fuel.
Conclusion:
Perform unit conversion of temperature at state 1 from degree Celsius to Kelvin.
For air temperature enter in the combustion chamber,
For then liquid injected temperature in the combustion chamber,
For air temperature exit in the combustion chamber,
Write the combustion equation of 1 kmol for
Here, liquid octane is
Express the stoichiometric coefficient of air by
Substitute
Refer Appendix Table A-18, A-19, A-20, and A-23, obtain the enthalpy of formation, at 298 K, 600 K, and 1500 K for
Substance | ||||
-249,950 | --- | --- | --- | |
0 | 8682 | 17,929 | 49,292 | |
0 | 8669 | 17,563 | 47,073 | |
-241,820 | 9904 | --- | 57,999 | |
-393,520 | 9364 | --- | 71,078 |
Refer Equation (X), and write the number of moles of reactants.
Here, number of moles of reactant octane, oxygen and nitrogen is
Refer Equation (X), and write the number of moles of products.
Here, number of moles of product carbon dioxide, water, oxygen and nitrogen is
Substitute the value of substance in Equation (II).
Therefore the heat transfer for
Substitute 8 for
Refer Equation (VI) for reactant and product to calculation the entropy in tabular form as:
For reactant entropy,
Substance |
(T, 1 atm) | ||||
1 | --- | 466.73 | 14.79 | 451.94 | |
21.25 | 0.21 | 226.35 | 1.81 | 4771.48 | |
79.9 | 0.79 | 212.07 | 12.83 | 15,919.28 | |
For product entropy,
Substance |
(T, 1 atm) | ||||
8 | 0.0757 | 292.11 | -6.673 | 2390.26 | |
9 | 0.0852 | 250.45 | -5.690 | 2305.26 | |
8.75 | 0.0828 | 25.97 | -5.928 | 2309.11 | |
79.9 | 0.7563 | 241.77 | 12.46 | 18,321.87 | |
Substitute
Substitute
Substitute
Thus, the entropy generation from the combustion chamber per unit mass of fuel is
(b)
The exergy destruction from the combustion chamber per unit mass of fuel.
Answer to Problem 92P
The exergy destruction from the combustion chamber per unit mass of fuel is
Explanation of Solution
Determine the exergy destruction from the combustion chamber per unit mass of the fuel.
Conclusion:
Substitute
Thus, the exergy destruction from the combustion chamber per unit mass of fuel is
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Chapter 15 Solutions
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