91Ó°ÊÓ

Combustion reactions are crucial in thermodynamics, especially when we are looking at energy production through burning fuels. When a fuel like butane (\text{C}_4 \text{H}_{10}) combusts in the presence of oxygen (\text{O}_2), it produces carbon dioxide (\text{CO}_2) and water (\text{H}_2 \text{O}). The balanced chemical equation for the complete combustion of butane is:\[ \text{C}_4 \text{H}_{10} + 6.5\text{O}_2 \rightarrow 4\text{CO}_2 + 5\text{H}_2 \text{O} \]This equation represents the theoretical amount of oxygen required for the reaction. Since we are discussing complete combustion, it means all the carbon in butane reacts with oxygen to form carbon dioxide, and all the hydrogen reacts to form water. Any deviation from this, like incomplete combustion, would lead to other byproducts like carbon monoxide.

In real-world applications, we often supply more air than theoretically required to ensure complete combustion. This additional air is quantified as 'excess air'. In this problem, we have 40% excess air. To calculate the actual oxygen required, we start from the theoretical requirement and adjust for the excess:\[ \text{Excess Air} = \frac{\text{Actual Air} - \text{Theoretical Air}}{\text{Theoretical Air}} \times 100 \]Given the theoretical requirement of 6.5 moles of \text{O}_2 for butane combustion, the actual oxygen needed is:\[ \text{Actual Oxygen} = 6.5 \times 1.40 = 9.1 \text{ moles of } \text{O}_2 \]Thus, the adjusted combustion reaction becomes:\[ \text{C}_4\text{H}_{10} + 9.1\text{O}_2 \rightarrow 4\text{CO}_2 + 5\text{H}_2 \text{O} + 2.6\text{O}_2 \]This ensures that there is enough oxygen present to burn all the fuel completely, even if the air supply is not perfectly mixed.

Enthalpy calculations are essential to find the heat transfer involved in a combustion process. Enthalpy measures the total heat content of a system. We need to determine specific enthalpies of reactants and products at given conditions. For butane combustion, reactants and products are initially at standard conditions (25°C and 100 kPa), and products are at 1000K. Specific heat capacities at constant pressure (\text{Cp}) help in this calculation.To find the enthalpy change, use:\[ \text{h}_{\text{initial}} = \text{h}_{25°C} + \text{c}_p (T - 298) \]To integrate from standard conditions to the required temperature, apply specific heat capacities:- \text{CO}_2 and \text{H}_2 \text{O} data at various temperatures, ensuring accurate increments.This leads us to the enthalpy values for components at 1000K, essential for further energy balance calculations. Finally, apply:\[ Q = \text{Output Enthalpy} - \text{Input Enthalpy} \]Subtract the total input enthalpy from the total output enthalpy to get the heat transfer. This process is repeated for different humidity conditions to analyze the effect.

Humidity can significantly influence combustion processes. In this problem, we look at how different humidity levels (90%, 70%, 50%) affect combustion of butane. Humidity involves the presence of water vapor in air, influencing the partial pressure and total mass of reactants. The partial pressure of water vapor at a given temperature is calculated using:\[ \text{Partial Pressure} = \text{Humidity Fraction} \times \text{Saturation Pressure at 25°C} \]At 25°C, the saturation pressure of water is approximately 3.17 kPa. Using this, we find partial pressures for each humidity level:

• 90%: 2.85 kPa
• 70%: 2.22 kPa
• 50%: 1.58 kPa

These values adjust the composition of intake air, affecting the total mass balance. Higher humidity means more water vapor, leading to less available oxygen from the same volume of air. Hence, combustion efficiency and heat transfer rates vary with humidity.