
The higher and lower heating values of a coal.

Answer to Problem 45P
The higher and lower heating values of a coal is
Explanation of Solution
Express the total mass of the coal when the ash is substituted.
Here, mass of ash is
Express the mass fraction of carbon.
Here, mass of carbon is
Express the mass fraction of hydrogen.
Here, mass of hydrogen is
Express the mass fraction of oxygen.
Here, mass of oxygen is
Express the mass fraction of nitrogen.
Here, mass of nitrogen is
Express the mass fraction of sulphur.
Here, mass of sulphur is
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.
Express the heat transfer from the combustion chamber.
Here, number of moles of products is
Express apparent molecular weight of the coal.
Here, number of moles of carbon, hydrogen, oxygen, nitrogen and sulfur is
Express higher value of coal.
Express lower value of coal.
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
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Express the combustion equation.
Perform the species balancing:
Oxygen balance:
Nitrogen balance:
Substitute
Refer Equation (XIII) and write the number of moles of carbon dioxide, water and sulfur oxide.
Refer Table A-26, “enthalpy of formation, Gibbs function of formation and entropy at
Substitute
Refer Equation (XXIII), and write the number of moles.
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Hence, the higher heating value of a coal is
For the LHV (lower heating value), the water in the products is taken to be vapor.
Refer Table A-26, “enthalpy of formation, Gibbs function of formation and entropy at
Substitute
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Hence, the lower heating value of a coal is
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Chapter 15 Solutions
Thermodynamics: An Engineering Approach
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