Flue-gas mass per kilogram of fuel – carbon balance method In ultimate analysis calculations, the mass of dry flue gas per kilogram of fuel can be expressed as the ratio of which two masses?

Introduction / Context:
Determining the amount of flue gas generated per kilogram of fuel is a common step in combustion calculations. One reliable approach uses a carbon balance, because essentially all fuel carbon appears in the products as CO2 and CO (for complete combustion, almost all as CO2).

Given Data / Assumptions:

• Dry flue gas basis (water vapour removed) is used.
• All carbon in the fuel exits in the dry flue gas as CO2 (and possibly CO if incomplete, but measured in analysis).
• Elemental conservation applies exactly: input carbon equals output carbon.

Concept / Approach:
If m_fg is the mass of dry flue gas per kg of fuel, and if (C_fuel) is the mass of carbon in 1 kg of fuel, while (C_per_kg_fg) is the mass of carbon present in 1 kg of dry flue gas (obtainable from gas analysis), then by carbon balance: C_fuel = m_fg * C_per_kg_fg, hence m_fg = C_fuel / C_per_kg_fg.

Step-by-Step Solution:
Define C_fuel = mass of C in 1 kg fuel (kg C/kg fuel).From gas analysis, find C_per_kg_fg (kg C/kg dry flue gas).Apply conservation: C_fuel = m_fg * C_per_kg_fg → m_fg = C_fuel / C_per_kg_fg.Recognize that this equals “mass of carbon in 1 kg of fuel” divided by “mass of carbon in 1 kg of flue gas.”

Verification / Alternative check:
An equivalent oxygen-balance approach is possible but is more sensitive to incomplete combustion and to moisture; the carbon balance on a dry basis is robust.

Why Other Options Are Wrong:

• The oxygen-based ratios reverse numerator/denominator and are not generally used in this simple form.
• Using nitrogen from fuel is inappropriate because fuel-bound nitrogen is small and most nitrogen in products comes from air.
• Option (d) inverts the correct ratio, yielding m_fg inverse.

Common Pitfalls:
Mixing wet and dry gas bases or forgetting that nearly all nitrogen in flue gas originates from the oxidizer (air), not the fuel.

Final Answer:
mass of carbon in 1 kg of fuel to the mass of carbon in 1 kg of flue gas