Question

Acetylene gas \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\) is burned completely with 20 percent excess air during a steady-flow combustion process. The fuel and the air enter the combustion chamber separately at \(25^{\circ} \mathrm{C}\) and 1 atm, and heat is being lost from the combustion chamber to the surroundings at \(25^{\circ} \mathrm{C}\) at a rate of 300,000 \(\mathrm{kJ} / \mathrm{kmol} \mathrm{C}_{2} \mathrm{H}_{2} .\) The combustion products leave the combustion chamber at 1 atm pressure. Determine \((a)\) the temperature of the products, \((b)\) the total entropy change per \(\mathrm{kmol}\) of \(\mathrm{C}_{2} \mathrm{H}_{2}\) and \((c)\) the exergy destruction during this process.

Short answer

(b) What is the total entropy change per kmol of acetylene? (c) What is the exergy destruction during this process?

Step-by-step solution

Calculate the amount of air required for complete combustion

To determine the amount of air required for complete combustion, we need to find out the stoichiometric equation for the combustion process. The balanced equation for the combustion of acetylene is given by: $$\mathrm{C}_{2}\mathrm{H}_{2} + \frac{5}{2}\mathrm{O}_{2}\to 2\mathrm{CO}_{2} + \mathrm{H}_{2}\mathrm{O}$$ So, for every kmol of acetylene, \(\frac{5}{2}\) kmol of oxygen is required.

Calculate the amount of excess air and determine the combustion products

Since 20% excess air is used in the combustion process, we can calculate the amount of excess oxygen as follows: Excess oxygen = 0.2 × \(\left(\frac{5}{2}\right)\) kmol = 0.5 kmol Total oxygen entering the chamber = \(\frac{5}{2} + 0.5\) = 3 kmol Since air consists of approximately 21% oxygen and 79% nitrogen by volume, we can determine the amount of nitrogen in the air: Amount of N\(_{2}\) = \(\frac{\text{Total oxygen}}{0.21} \times 0.79\) = 11.24 kmol Now we can determine the combustion products. After combustion, we will have the following products: - 2 kmol of CO\(_{2}\) - 1 kmol of H\(_{2}\)O - 0.5 kmol of excess O\(_{2}\) - 11.24 kmol of N\(_{2}\)

Perform an energy balance to find the temperature of the products

To find the temperature of the products, we need to perform an energy balance on the combustion chamber. For complete combustion and neglecting the kinetic and potential energy changes: $$\text{Heat in} - \text{Heat out} = \text{Heat of formation} + \text{Heat absorbed by the products}$$ Using the given heat loss of 300,000 kJ/kmol C\(_{2}\)H\(_{2}\), the balance equation becomes: $$\text{Heat of formation} - 300,000 = m_{\text{CO}_{2}}c_{p} \text{(T}_{\text{products}} - 298\text{)} + m_{\text{H}_{2}\text{O}}c_{p} \text{(T}_{\text{products}} - 298\text{)} + m_{\text{O}_{2}}c_{p} \text{(T}_{\text{products}} - 298\text{)} + m_{\text{N}_{2}}c_{p} \text{(T}_{\text{products}} - 298\text{)}$$ Considering the constants of \(c_{p}\), we can solve for the product temperature, T\(_{\text{products}}\) (K).

Calculate the total entropy change

To calculate the entropy change, we need to find the entropy change of the products and subtract the entropy change of the reactants: $$\Delta S_{\text{total}} = \Delta S_{\text{products}} - \Delta S_{\text{reactants}}$$ This can be calculated using the specific entropies of the substances (assumed to be constant) and the temperatures of the reactants and products.

Calculate the exergy destruction

Exergy destruction is the difference between the exergy of the reactants and products, taking into account the work potential of the products: $$\text{Exergy destruction} = \text{Exergy}_{\text{reactants}} - \text{Exergy}_{\text{products}}$$ This can be calculated using the given temperature and pressure conditions, as well as the temperature and pressure of the products. By completing all these steps, we will have determined the temperature of the products, the total entropy change per kmol of acetylene, and the exergy destruction during this steady-flow combustion process.