Question

Propane fuel \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)\) is burned with an air-fuel ratio of 25 in an atmospheric pressure heating furnace. Determine the heat transfer per kilogram of fuel burned when the temperature of the products is such that liquid water just begins to form in the products.

Short answer

#tag_title# Calculation#tag_content# Let's perform the calculation to find the heat transfer per kg of fuel: First, calculate the mass of combustion products per kg of propane: Mass of CO2 = 3 * 44/12 kg/mol (mass of 3 moles of CO2) Mass of H2O = 4 * 18/2 kg/mol (mass of 4 moles of H2O) Mass of O2 = (25-5)*32/32 kg/mol (mass of 20 moles of O2) Mass of N2 = (25*(21%/79%)-5)*28/28 kg/mol (mass of (25-5)/0.21-5 moles of N2) Now, calculate the heat absorbed by the combustion products: Heat absorbed by CO2 = mass of CO2 * 0.85 kJ/kg K * 100 K Heat absorbed by H2O = mass of H2O * 4.18 kJ/kg K * 100 K Heat absorbed by O2 = mass of O2 * 0.92 kJ/kg K * 100 K Heat absorbed by N2 = mass of N2 * 1.04 kJ/kg K * 100 K Sum the heat absorbed by each combustion product: Total heat absorbed = Heat absorbed by CO2 + Heat absorbed by H2O + Heat absorbed by O2 + Heat absorbed by N2 Finally, calculate the heat transfer per kg of fuel: Heat transfer per kg of fuel = (46.3*10^6 - Total heat absorbed) / mass of fuel burned Heat transfer per kg of fuel = (46.3*10^6 - Total heat absorbed) / 1kg (as we are calculating per kg of fuel) By performing these calculations, we find the heat transfer per kilogram of fuel burned when propane is burned with an air-fuel ratio of 25.

Step-by-step solution

Write the balanced combustion equation

We will first write the balanced combustion reaction for propane. Propane reacts with oxygen, O2, to form combustion products: carbon dioxide, CO2, and water, H2O. The balanced equation is : C3H8 + 5O2 -> 3CO2 + 4H2O

Determine the actual combustion equation given the air-fuel ratio

Now, determine the actual combustion equation. The air-fuel ratio is given as 25, and air consists of approximately 21% O2 and 79% N2. So, we can rewrite the balanced equation as: C3H8 + 5(O2) * 25 -> 3CO2 + 4H2O + (25-5)*(O2) + (25*(21%/79%)-5)*(N2)

Find the products' temperature when liquid water starts forming

We need to find the temperature when liquid water starts forming in the products. The initial temperature of the products can be assumed to be the same as that of the surroundings, which is at atmospheric pressure (1 atm). The products will heat up as the heat is released from the combustion process. To find the temperature when liquid water just starts to form, we will look at the phase change diagram for water and find the temperature at which liquid water and vapor water coexist at 1 atm pressure. That temperature is the boiling point of water, which is 100°C.

Calculate the heat released during combustion

Now, we need to calculate how much heat is released during the combustion process. For that, we need the Enthalpy of Combustion value (ΔHC) of propane. From standard values, we know the lower heating value (LHV) of propane is 46.3 MJ/kg.

Calculate the heat transfer per kilogram of fuel burned

Once we know the amount of heat released per kilogram of fuel burned, we can now calculate the heat transfer per kilogram of fuel burned. Given that LHV of propane = 46.3 MJ/kg, and assuming that the heat released is entirely absorbed by the system (no heat loss to the surroundings), we can use the following formula to calculate the heat transfer per kilogram of fuel: Heat transfer per kg of fuel = ΔHC * mass of fuel burned Now, we need to account for the heat being absorbed by the products to reach the temperature when the liquid water just starts forming (100°C). We account for the sensible heat absorbed by the products to reach that temperature using specific heat capacities. We will assume constant specific heat capacities for the combustion products: CO2 (0.85 kJ/kg K), H2O (4.18 kJ/kg K, for liquid water), O2 (0.92 kJ/kg K), and N2 (1.04 kJ/kg K). Heat absorbed by CO2 = mass of CO2 * specific_heat_CO2 * temperature_change Heat absorbed by H2O = mass of H2O * specific_heat_H2O * temperature_change Heat absorbed by O2 = mass of O2 * specific_heat_O2 * temperature_change Heat absorbed by N2 = mass of N2 * specific_heat_N2 * temperature_change Now, subtract the heat absorbed by the combustion products from the heat released during combustion: Heat transfer per kg of fuel = (Heat released during combustion - Heat absorbed by the combustion products) / mass of fuel burned By plugging in the values into this equation, the heat transfer per kilogram of fuel burned can be calculated.