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Complete combustion happens when a fuel completely reacts with oxygen, leaving no unburned carbon or partially oxidized products like carbon monoxide. This process exclusively produces carbon dioxide \(\text{CO}_2\) and water \(\text{H}_2O\). For instance, during the combustion of ethane \(\text{C}_2\text{H}_6\), the balanced reaction in its complete form is: \[ \text{C}_2\text{H}_6 + \frac{7}{2}\text{O}_2 + 3.76\times\frac{7}{2} \text{N}_2 \rightarrow 2\text{CO}_2 + 3\text{H}_2\text{O} + 3.76 \times \frac{7}{2} \text{N}_2. \]Complete combustion ensures maximum energy release from the fuel, typically translating to higher efficiency in energy systems. However, achieving complete combustion often requires ensuring the correct air-to-fuel ratio and sufficiently high combustion temperatures.

Incomplete combustion occurs when the fuel does not completely react with oxygen. This can result in partially oxidized products like carbon monoxide (CO) and even unburned hydrocarbons. For example, the incomplete combustion of ethane with 95% of the carbon converting to carbon dioxide and 5% to carbon monoxide is represented as: \[ \text{C}_2\text{H}_6 + a \text{O}_2 + 3.76a \text{N}_2 \rightarrow 0.95 \times 2\text{CO}_2 + 0.05 \times 2\text{CO} + 3\text{H}_2\text{O} + 3.76a \text{N}_2. \]In this process, the efficiency drops because not all carbon atoms form \(\text{CO}_2\), leading to lesser energy being released compared to complete combustion. Incomplete combustion often produces pollutants like carbon monoxide, which is hazardous to health and contributes to environmental degradation.

The enthalpy change, \( \triangle H \), during a combustion reaction represents the heat transfer when the process occurs at constant pressure. It is calculated by summing the enthalpies of the products and then subtracting the enthalpies of the reactants. For instance, the enthalpy of the reactants at initial temperature (500 K for theoretical air and ethane) must be calculated and compared with the enthalpy of the products at final temperature (1000 K). The enthalpy change formula is: \[ \triangle H = H_{\text{products}} - H_{\text{reactants}}. \]This allows us to understand the energy exchange involved in the reaction. For the complete combustion of ethane, the products are \( \text{CO}_2\) and \( \text{H}_2\text{O} \), whereas for incomplete combustion, both \( \text{CO}_2 \) and \( \text{CO} \) are included in the enthalpy calculations.

In steady-flow systems, such as combustion processes in turbines or engines, the Steady-Flow Energy Equation (SFEE) helps to quantify the energy changes. The SFEE is given by: \[ Q - W = \frac{d H_{\text{products}} - d H_{\text{reactants}}}{d T}. \]Here, \( Q \) is the heat transferred into the system, \( W \) is the work done by the system. For combustion problems, it's often applicable to assume \( W = 0 \) (no work done), simplifying the equation to: \[ Q = \frac{d H_{\text{products}} - d H_{\text{reactants}}}{d T}.\] This equation is crucial for determining important properties such as temperature, pressure, and heat transfer in a steady combustion system. Understanding and applying SFEE allows engineers to design efficient systems by better controlling the combustion process and optimizing energy yields.

The theoretical air requirement is the exact quantity of air needed for the complete combustion of a given amount of fuel. In our example of ethane, it’s calculated using stoichiometry. For ethane, the stoichiometric equation tells us: \[ \text{C}_2\text{H}_6 + \frac{7}{2}\text{O}_2 + \text{3.76}\frac{7}{2}\text{N}_2 \rightarrow 2\text{CO}_2 + 3\text{H}_2\text{O} + 3.76 \times \frac{7}{2} \text{N}_2. \]From this, the theoretical \( \text{O}_2 \) needed is \(\frac{7}{2} \) moles. Usually, combustion processes use more than the theoretical amount to ensure complete reaction, called 'excess air'. In this problem, we are provided with 150% theoretical air, which means multiplying the theoretical air by 1.5. This determines the actual air-fuel mixture, affecting efficiency and the outcome in terms of produced gases during combustion. Efficient system designs rely on these calculations to optimize fuel usage and minimize pollutants.