Repeat Prob. 15–112 using a coal from Utah that has an ultimate analysis (by mass) of 61.40 percent C, 5.79 percent H2, 25.31 percent O2, 1.09 percent N2, 1.41 percent S, and 5.00 percent ash (noncombustibles).
(a)
The amount of steam generated per unit of fuel mass burned.
Answer to Problem 109RP
The amount of steam generated per unit of fuel mass burned is
Explanation of Solution
Express the number of moles of carbon.
Here, molar mass of carbon is
Express the number of moles of hydrogen.
Here, molar mass of hydrogen is
Express the number of moles of oxygen.
Here, molar mass of oxygen is
Express the number of moles of nitrogen.
Here, molar mass of nitrogen is
Express the number of moles of sulphur.
Here, molar mass of sulphur is
Express the total number of moles.
Express the mole fraction of carbon.
Express the mole fraction of hydrogen.
Express the mole fraction of oxygen.
Express the mole fraction of nitrogen.
Express the mole fraction of sulphur.
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
Write the formula for the amount of steam generated per unit mass of fuel burned.
Here, the mass of the steam is
Conclusion:
Refer Table A-1, “molar mass, gas constant, and the critical point properties”, and write the molar masses.
Here, molar mass of air is
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Express the combustion equation.
Here, carbon dioxide, water, sulfur dioxide, nitrogen and oxygen is
Perform the species balancing according to the oxygen balance:
Oxygen balance:
Substitute
Calculate the apparent molecular weight of the cool.
Refer Appendix Table A-18, A-19, A-20, and A-23, obtain the enthalpy of formation, at 298 K , and 500 K for
Substance | |||
0 | 8682 | 14,770 | |
0 | 8669 | 14,581 | |
-241820 | 9904 | 16,828 | |
-393,520 | 9364 | 17,678 |
Substitute the value of substance in Equation (XIII).
Calculate the heat loss per unit mass of the fuel.
Substitute
Thus, the amount of steam generated per unit of fuel mass burned is
(b)
The change in the exergy of the combustion steams, in
Answer to Problem 109RP
The change in the exergy of the combustion steams, in
Explanation of Solution
Write the expression for entropy generation during this process.
Write the combustion equation of Equation (VI)
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 change of the combustion steam is equal to the exergy destruction.
Here, the thermodynamic temperature of the surrounding is
Conclusion:
Refer Equation (XIX) for reactant and product to calculation the entropy in tabular form as:
For reactant entropy,
Substance |
(T, 1 atm) | ||||
0.5758 | 0.5758 | 5.74 | -4.589 | 5.95 | |
0.3258 | 0.3258 | 130.68 | -9.324 | 45.61 | |
0.0890 | 0.0890 | 205.04 | -20.11 | 20.04 | |
0.00438 | 0.00438 | 191.61 | -45.15 | 1.04 | |
0.9821 | 0.21 | 205.04 | -12.98 | 214.12 | |
3.693 | 0.79 | 191.61 | -1.960 | 714.85 | |
For product entropy,
Substance |
(T, 1 atm) | ||||
0.5758 | 0.1170 | 234.814 | -17.84 | 145.48 | |
0.3258 | 0.0662 | 206.413 | -22.57 | 74.60 | |
0.3274 | 0.0665 | 220.589 | -22.54 | 79.60 | |
3.693 | 0.7503 | 206.630 | -2.388 | 771.90 | |
Substitute
Substitute
Calculate the exergy destruction per unit mass of the basis.
Thus, the change in the exergy of the combustion steams, in
(c)
The exergy change of the steam, in
Answer to Problem 109RP
The exergy change of the steam, in
Explanation of Solution
Determine the exergy change of the steam stream.
Here, the final enthalpy is
Conclusion:
Substitute
Thus, the exergy change of the steam, in
(d)
The lost work potential, in
Answer to Problem 109RP
The lost work potential, in
Explanation of Solution
Determine the lost work potential is the negative of the net exergy change both streams.
Conclusion:
Substitute
Thus, the lost work potential, in
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