Methane gas is burned completely with 30 % excess air at...

Methane gas is burned completely with $30 \%$ excess air at approximately atmospheric pressure. Both the methane and the air enter the furnace at $303.15 \mathrm{K}\left(30^{\circ} \mathrm{C}\right)$ saturated with water vapor, and the flue gases leave the furnace at $1773.15 \mathrm{K}\left(1500^{\circ} \mathrm{C}\right)$. The flue gases then pass through a heat exchanger from which they emerge at $323.15 \mathrm{K}\left(50^{\circ} \mathrm{C}\right)$ Per mole of methane, how much heat is lost from the furnace, and how much heat is transferred in the heat exchanger?

Key Concepts

Stoichiometry of Combustion Reactions

This concept involves writing and balancing the chemical equation for the complete combustion of a fuel – in this case, methane (CH4) – in oxygen. It includes determining the molar ratios of reactants and products, considering all species formed (such as CO2, H2O, and inert gases present in air). Proper stoichiometry is crucial to understand how much oxygen is required for complete combustion, and it lays the groundwork for energy calculations related to the reaction.

Excess Air

Excess air refers to supplying more air (and thus oxygen) than the stoichiometric requirement needed for complete combustion. In many practical combustion systems, excess air is used to ensure complete oxidation of the fuel, avoiding the formation of carbon monoxide or soot. However, the additional air carries extra thermal mass and influences the energy balance by absorbing and carrying away some of the heat, thereby affecting the overall efficiency of the process.

Sensible Enthalpy Change

Sensible enthalpy change accounts for the energy required to raise the temperature of a substance without a phase change. In the context of a combustion system, it is important to calculate how much energy is absorbed or released as the reactants and products are heated from one temperature to another. This includes the heating of gases such as combustion products and air, and is typically obtained by integrating specific heat capacities over the temperature range of interest.

Heat Exchanger Performance

The performance of a heat exchanger in a combustion system can be evaluated by determining how much sensible heat is recovered from the hot flue gases before they are released to the environment. The analysis involves calculating the temperature drop of the gases and the corresponding reduction in enthalpy. This retrieved heat can be useful in improving the system’s overall thermal efficiency, though it also requires careful consideration of the changes in gas composition and heat transfer properties.

Energy Balances in Thermal Systems

An overall energy balance in a combustion process allows for the determination of heat losses and recoveries. It involves accounting for the energy released from combustion and subsequently distributed among various components, such as the heat lost from the furnace (including losses due to hot flue gases) and the heat transferred in the heat exchanger. This concept is central to designing efficient combustion systems and optimizing the thermal management in industrial processes.

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