A fuel gas consisting of 94 mole- % methane and 6 mole- %...

A fuel gas consisting of 94 mole- $\%$ methane and 6 mole- $\%$ nitrogen is burned with $35 \%$ excess air in a continuous water heater. Both fuel gas and air enter dry at $298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$. Water is heated at a rate of $34.0 \mathrm{~kg} \mathrm{~s}^{-1}$ from $298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$ to $368.15 \mathrm{~K}\left(95^{\circ} \mathrm{C}\right)$. The flue gases leave the heater at $483.15 \mathrm{~K}\left(210^{\circ} \mathrm{C}\right)$. Of the entering methane, $70 \%$ burns to carbon dioxide and $30 \%$ burns to carbon monoxide. What volumetric flow rate of fuel gas is required if there are no heat losses to the surroundings?

Key Concepts

Energy Balance

An energy balance involves equating the energy provided by the fuel combustion to the energy absorbed by the process, such as heating water. It requires setting up the conservation of energy equation where the energy released from chemical reactions is matched by the sensible heat gained by the fluid, accounting for temperature changes across the system.

Combustion Stoichiometry

Combustion stoichiometry is the calculation of the reactants and products in a combustion reaction according to the chemical equations. It involves balancing the number of atoms in the reactants and products, considering complete or partial oxidation, and is essential for determining the required fuel and air quantities.

Excess Air Considerations

Excess air in a combustion process refers to the amount of air supplied beyond the stoichiometric requirement necessary for complete combustion. Its inclusion affects the concentrations of oxygen in the reaction, dilutes the combustion products, and influences the temperature and efficiency of the process.

Fuel Gas Composition

The fuel gas composition specifies the proportions of different components present in the fuel, which directly affect its calorific value and combustion characteristics. Understanding the mixture's composition is crucial for accurate stoichiometric calculations and determining the overall heat release during combustion.

Thermochemical Data

Thermochemical data, such as heats of combustion and enthalpy changes, are essential for quantifying the energy outcomes of chemical reactions. These values provide the basis for calculating the energy available from fuel combustion and for designing systems that utilize this energy effectively.

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