A steam boiler heats liquid water at 200°C to superheated steam at 4 MPa and 400°C. Methane fuel (CH4) is burned at atmospheric pressure with 50 percent excess air. The fuel and air enter the boiler at 25°C and the products of combustion leave at 227°C. Calculate (a) the amount of steam generated per unit of fuel mass burned, (b) the change in the exergy of the combustion streams, in kJ/kg fuel, (c) the change in the exergy of the steam stream, in kJ/kg steam, and (d) the lost work potential, in kJ/kg fuel. Take T0 = 25°C.
(a)
The amount of steam generated per unit of fuel mass burned.
Answer to Problem 112RP
The amount of steam generated per unit of fuel mass burned 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
Determine the amount of steam generated per unit mass of fuel burned from an energy balance.
Here, the mass of the steam is
Conclusion:
Perform unit conversion of temperature at state 1 from degree Celsius to Kelvin.
For air temperature enter in the machine,
For air temperature exit from the machine,
Write the combustion equation of 1 kmol for
Here, liquid methane is
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 | |||
-74,850 | --- | --- | |
0 | 8682 | 14,770 | |
0 | 8669 | 14,581 | |
-241820 | 9904 | 16,828 | |
-393,520 | 9364 | 17,678 |
Refer Equation (V), and write the number of moles of reactants.
Here, number of moles of reactant methane, oxygen and nitrogen is
Refer Equation (V), 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 1 for
Calculate the heat loss per unit mass of the fuel.
From the table A-4, “Saturated water-Temperature” obtain the value of the saturated enthalpy and entropy of liquid at the
From the table A-6, “Superheated water” obtain the value of the enthalpy and entropy at the
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 112RP
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 (VIII) for reactant and product to calculation the entropy in tabular form as:
For reactant entropy,
Substance |
(T, 1 atm) | ||||
1 | --- | 186.16 | --- | 186.16 | |
3 | 0.21 | 205.04 | -12.98 | 654.06 | |
11.28 | 0.79 | 191.61 | -1.960 | 2183.47 | |
For product entropy,
Substance |
(T, 1 atm) | ||||
1 | 0.0654 | 234.814 | -22.67 | 257.48 | |
2 | 0.1309 | 206.413 | -16.91 | 446.65 | |
1 | 0.0654 | 220.589 | -22.67 | 243.26 | |
11.28 | 0.7382 | 206.630 | -2.524 | 2359.26 | |
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 112RP
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 112RP
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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