Question

Propane gas \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)\) enters a steady-flow combustion chamber at 1 atm and \(25^{\circ} \mathrm{C}\) and is burned with air that enters the combustion chamber at the same state. Determine the adiabatic flame temperature for \((a)\) complete combustion with 100 percent theoretical air, ( \(b\) ) complete combustion with 200 percent theoretical air, and \((c)\) incomplete combustion (some \(\mathrm{CO}\) in the products) with 90 percent theoretical air.

Short answer

Question: Determine the adiabatic flame temperature for the combustion of propane gas under the following conditions: (a) complete combustion with 100% theoretical air, (b) complete combustion with 200% theoretical air, and (c) incomplete combustion with 90% theoretical air. Answer: To determine the adiabatic flame temperature for each case, follow these steps: 1. Write the balanced chemical reactions for complete and incomplete combustion of propane. 2. Calculate the moles of reactants involved in each case: 100% theoretical air, 200% theoretical air, and 90% theoretical air. 3. Using the heat capacities at constant pressure (Cp) and the enthalpy of formation for the combustion reactions, set up equations to solve for the final temperature (Tf) for each case. By solving Tf for each case, you will obtain the adiabatic flame temperature for complete combustion with 100% theoretical air, complete combustion with 200% theoretical air, and incomplete combustion with 90% theoretical air.

Step-by-step solution

: (a) 100% theoretical air As per the complete combustion reaction, for each mole of propane, we require 5 moles of oxygen. Moles of propane, \(n_{C3H8} = 1\) Moles of oxygen, \(n_{O2} = 5\) (b) 200% theoretical air Air contains approximately 21% oxygen, so we need twice the amount of theoretical air for combustion. Moles of oxygen, \(n_{O2} = 5 \times 2 = 10\) (c) 90% theoretical air We will use the incomplete combustion reaction as given. Moles of propane, \(n_{C3H8} = 1\) Moles of oxygen, \(n_{O2} = 5 \times 0.9 = 4.5\) #Step 3: Determine the adiabatic flame temperature#

: To determine the adiabatic flame temperature, we need to calculate the heat generated during combustion for each case and assume that all the heat is absorbed by the reactants and the products. We'll use the heat capacities at constant pressure (\(C_p\)) of each species and the enthalpy of formation for the combustion reactions. (a) 100% theoretical air Heat gained = Heat lost \[C_3H_8 + 5O_2 \to 3CO_2 + 4H_2O\] \[ \Delta H_{reactants} = \Delta H_{products}\] \[C_{p, C3H8} \times (T_{f}-298)+ 5C_{p, O2} \times (T_{f}-298) = 3C_{p, CO2} \times (T_{f}-298) + 4C_{p, H2O} \times (T_{f}-298)\] Solve the equation for T_f for 100% theoretical air. (b) 200% theoretical air Repeat the process as in (a) with the new moles of oxygen and solve for T_f for 200% theoretical air. (c) Incomplete combustion (90% theoretical air) \[C_3H_8 + 4.5O_2 \to 2CO_2 + CO + 4H_2O\] Repeat the process as in (a) using the incomplete combustion reaction and the new moles of oxygen. Solve for T_f for 90% theoretical air. By solving T_f for each case, we'll obtain the adiabatic flame temperature for complete combustion with 100% theoretical air, complete combustion with 200% theoretical air, and incomplete combustion with 90% theoretical air.