Let's break down and solve **CS 9.8** step by step. *Note: Since the full problem data (like fuel composition, enthalpy values, etc.) is not given in the screenshot, I’ll explain the general approach and provide a sample calculation assuming typical values. You can plug in your actual values as needed.* --- ### **CS 9.8: Step-by-Step Solution** **Problem Restatement:** > Determine the effect of the percent excess air fed to the boiler furnace by calculating the rate of steam generation (kg/min) for air flow rates that are 5% and 25% in excess of that theoretically required. Speculate on the reason for choosing 15% excess air in the prescribed process by giving one possible reason for not using less air and one for not using more. --- #### **Step 1: Write the Combustion Reaction** Suppose you are burning coal with the general formula: CₓHᵧ + O₂ → CO₂ + H₂O For this example, let's assume you have a known mass of fuel (say, 1 kg) and its elemental analysis. Let’s use pure carbon for simplicity: C + O₂ → CO₂ --- #### **Step 2: Calculate Theoretical Air Required** - **Find stoichiometric oxygen required:** 1 mole C needs 1 mole O₂ → 12 g C needs 32 g O₂ - **For 1 kg C:** \[ \text{O}_2 \text{ required} = \frac{32}{12} \times 1\,\text{kg} = 2.67\,\text{kg} \] - **Air contains ~23% O₂ by mass:** \[ \text{Theoretical air required} = \frac{2.67\,\text{kg O}_2}{0.23} = 11.6\,\text{kg} \] --- #### **Step 3: Calculate Excess Air Flow Rates** - **5% Excess Air:** \[ \text{Air supplied} = 11.6 \times 1.05 = 12.18\,\text{kg} \] - **25% Excess Air:** \[ \text{Air supplied} = 11.6 \times 1.25 = 14.5\,\text{kg} \] --- #### **Step 4: Effect on Steam Generation** - **The more excess air supplied, the more heat is used to warm up the extra air, not to generate steam.** - **Assume fixed heat input from fuel.** Let’s say total heat available = Q (from burning 1 kg of C). - **Heat to generate steam:** \[ Q = \text{Heat to raise steam} + \text{Heat to raise air temperature} \] - **With more excess air, less heat remains for steam generation.** - **Thus, steam generation decreases as excess air increases.** ##### **Illustrative Calculation:** Suppose: - Heat from 1 kg C = 33,000 kJ (heating value) - Air and products heated from 25°C to 200°C - Specific heat of air = 1.0 kJ/kg·K 1. **Heat to raise air temperature:** \[ Q_{\text{air}} = m_{\text{air}} \cdot C_p \cdot \Delta T \] - For 5% excess: \(12.18 \times 1.0 \times (200-25) = 12.18 \times 175 = 2,131\,\text{kJ}\) - For 25% excess: \(14.5 \times 1.0 \times 175 = 2,538\,\text{kJ}\) 2. **Heat available for steam:** - For 5% excess: \(33,000 - 2,131 = 30,869\,\text{kJ}\) - For 25% excess: \(33,000 - 2,538 = 30,462\,\text{kJ}\) 3. **Steam generated (assuming latent heat of vaporization = 2,260 kJ/kg):** - For 5% excess: \(30,869 / 2,260 = 13.66\,\text{kg}\) - For 25% excess: \(30,462 / 2,260 = 13.48\,\text{kg}\) --- #### **Step 5: Discussion - Why 15% Excess Air?** - **Not less than 15%:** Less excess air risks incomplete combustion (CO, soot, unburned fuel). - **Not more than 15%:** More excess air wastes heat to warm extra air, reducing boiler efficiency. --- ### **Final Answers (Sample Data):** - **Steam generation at 5% excess air:** **13.66 kg** - **Steam generation at 25% excess air:** **13.48 kg** - **Reason for 15% excess air:** Balances complete combustion (avoids CO/unburned fuel) and efficiency (minimizes heat loss to excess air). --- **Plug in your actual numbers for the fuel and conditions you have. The steps remain the same!** --- If you provide the fuel composition or more specific data, I can run the exact numbers for you.

Let's approach these two related questions step-by-step, providing a detailed explanation and assumptions to illustrate the methodology. Since the problem data isn't fully visible, I will outline the general process and use typical values to demonstrate calculations. You can substitute your actual data where needed. --- ## CS 9.8: Effect of Excess Air on Steam Generation ### **Step 1: Understand the Problem** - **Goal:** Calculate the rate of steam generation (kg/min) at two excess air levels: 5% and 25% - **Assumption:** The fuel burned is known; for simplicity, assume a representative fuel like coal with a known heating value and composition. --- ### **Step 2: Theoretical Air Calculation** - **Fuel example:** Assume burning 1 kg of carbon (C) for simplicity. - **Stoichiometric combustion:** \[ \text{C} + O_2 \rightarrow CO_2 \] - **Oxygen needed per kg of carbon:** \[ \text{O}_2 = \frac{32\, \text{g}}{12\, \text{g}} \times 1000\, \text{g} = 2.67\, \text{kg} \] - **Air required (since air is ~23% O₂ by mass):** \[ \text{Theoretical air} = \frac{2.67\, \text{kg}}{0.23} \approx 11.6\, \text{kg} \] --- ### **Step 3: Actual Air Flow Rates for Excess Air** - **At 5% excess air:** \[ \text{Air} = 11.6 \times 1.05 \approx 12.18\, \text{kg} \] - **At 25% excess air:** \[ \text{Air} = 11.6 \times 1.25 \approx 14.50\, \text{kg} \] --- ### **Step 4: Impact on Heat Available for Steam Generation** - **Total heat from fuel:** Assume, for example, 33,000 kJ/kg (typical for coal). - **Heat used to warm excess air:** - Specific heat capacity of air, \( C_{p} \approx 1\, \text{kJ/kg·K} \) - Temperature rise, \( \Delta T \), from ambient (~25°C) to flue gas temperature (assumed 200°C): \[ Q_{\text{air}} = m_{\text{air}} \times C_{p} \times \Delta T \] - **Calculations:** - For 5% excess: \[ Q_{air,5\%} = 12.18\, \text{kg} \times 1\, \text{kJ/kg·K} \times (200 - 25)^\circ C = 12.18 \times 175 = 2,131\, \text{kJ} \] - For 25% excess: \[ Q_{air,25\%} = 14.50 \times 175 = 2,538\, \text{kJ} \] - **Remaining heat for steam:** - For 5% excess: \[ Q_{steam} = 33,000 - 2,131 = 30,869\, \text{kJ} \] - For 25% excess: \[ Q_{steam} = 33,000 - 2,538 = 30,462\, \text{kJ} \] - **Steam generation:** - Latent heat of vaporization (approximate): 2,260 kJ/kg \[ \text{Steam} = \frac{Q_{steam}}{2,260} \] - For 5% excess: \[ \frac{30,869}{2,260} \approx 13.66\, \text{kg} \] - For 25% excess: \[ \frac{30,462}{2,260} \approx 13.48\, \text{kg} \] --- ### **Step 5: Convert to Rate (kg/min)** - Assume these are per batch or per hour; to find per minute, divide by appropriate time. - **If these are per hour:** \[ \text{Steam per min} = \frac{\text{kg per hour}}{60} \] - **Results:** | Excess Air | Steam per min (kg/min) | |--------------|------------------------| | 5% | \(\approx 13.66 / 60 \approx 0.23\) kg/min | | 25% | \(\approx 13.48 / 60 \approx 0.22\) kg/min | --- ## **Summary CS 9.8:** - Increasing excess air from 5% to 25% slightly decreases the steam generation rate because more heat is consumed warming the excess air rather than producing steam. - **Final note:** Actual values depend on fuel properties and operation specifics. --- ## CS 9.9: Flue Gas Temperature at the Heat Exchanger ### **Step 1: Understand the Task** - **Goal:** Estimate the flue gas temperature after the air preheater for 5% and 25% excess air, based on the oxygen content. - **Assumption:** The oxygen content in flue gases correlates with excess air; typical values might be: | Excess Air | O₂ in flue gas (%) | |--------------|---------------------| | 5% | ~3.5% | | 25% | ~8% | ### **Step 2: Heat Balance Approach** - The temperature of the flue gases depends on: - Heat transfer in the heat exchanger - The temperature of incoming gases - The amount of excess air (more air → higher flue gas temp) - **Basic relation:** The higher the oxygen content (more excess air), the higher the flue gas temperature after heat exchange, assuming the same heat transfer conditions. ### **Step 3: Estimation** - **Typical flue gas exit temperature:** For 5% excess air, about 150–200°C. - **For 25% excess air:** Slightly higher, around 200–250°C. **Approximate estimates:** | Excess Air | Flue Gas Temp (°C) | |--------------|---------------------| | 5% | 180°C | | 25% | 220°C | --- ## **Summary CS 9.9:** - Increasing excess air increases the flue gas temperature after the heat exchanger due to higher oxygen content and more heat carried away by the gases. - Precise calculation requires detailed heat transfer analysis and actual inlet conditions. --- ## **Final Remarks:** - The key takeaway is that excess air influences both the rate of steam generation and the temperature of flue gases. - Choosing around 15% excess air balances complete combustion with efficiency, avoiding excessive heat loss. --- **You can refine these estimates with your specific data (fuel composition, heat transfer coefficients, inlet temperatures, etc.).**