Question

Acetylene gas \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\) at \(25^{\circ} \mathrm{C}\) is burned during a steady-flow combustion process with 30 percent excess air at \(27^{\circ} \mathrm{C} .\) It is observed that \(75,000 \mathrm{kJ}\) of heat is being lost from the combustion chamber to the surroundings per kmol of acetylene. Assuming combustion is complete, determine the exit temperature of the product gases.

Short answer

Answer: To determine the exit temperature, we need to follow these steps: 1. Write the balanced combustion equation for acetylene gas with 30 percent excess air. 2. Apply the energy balance equation for steady-flow combustion. 3. Find the inlet enthalpy of the reactants using the inlet temperature of 27°C and standard enthalpy tables. 4. Calculate the outlet enthalpy and exit temperature using the energy balance equation and standard enthalpy tables. By following these steps and using the given heat loss, we can determine the exit temperature of the product gases.

Step-by-step solution

Write the balanced combustion equation

First, we need to write the balanced combustion equation for acetylene gas with 30 percent excess air. The stoichiometric amount of air required for the combustion reaction is: C2H2 + 2.5(O2 + 3.76N2) -> 2CO2 + H2O + 9.4N2 Since there is 30% excess air, the actual amount of air is 1.3 times the stoichiometric amount, so the balanced combustion equation becomes: C2H2 + 3.25(O2 + 3.76N2) -> 2CO2 + H2O + 0.75O2 + 12.22N2

Apply the energy balance equation

Now, we can apply the energy balance equation for steady-flow combustion. The heat loss is given as 75000 kJ per kmol of acetylene. The equation is: \(\dot{m}_{fuel}(h_{in} - h_{out}) - Q_{loss} = 0\) Rearrange for outlet enthalpy: \(h_{out} = h_{in} - \frac{Q_{loss}}{\dot{m}_{fuel}}\)

Find the inlet enthalpy of the reactants

Let's first find the inlet enthalpy of the reactants. Use the inlet temperature of 27°C (assume it to be equal for both acetylene and air) and find the enthalpy values of the components using standard enthalpy tables. Sum the enthalpies to get the total inlet enthalpy: \(h_{in} = m_{C2H2}h_{C2H2, 27^\circ C} + m_{air}h_{air, 27^\circ C}\)

Calculate the outlet enthalpy and exit temperature

Using the energy balance equation from Step 2, calculate the outlet enthalpy. \(h_{out} = h_{in} - \frac{75000\,\text{kJ}}{1\,\text{kmol}}\) Now, find the partial enthalpy values of the individual components in the product side from the outlet enthalpy and sum them to get the total outlet enthalpy. Use the total outlet enthalpy to find the exit temperature using standard enthalpy tables: T_exit = T_outlet Hence, we can determine the exit temperature of the product gases.