Using the steam generated versus the fuel consumed method, calculate the boiler efficiency of a coal plant that consumed 1,363,000,000 tons of 13,260 Btu/lb coal and generated 6,400,000 lb of steam for a month of operation.

- Feedwater temperature: 208 degrees F
- Steam conditions: 200 psig, superheated to 520 degrees F

To calculate the boiler efficiency of a coal plant, you can use the steam generated vs fuel consumed method. The energy input can be calculated using the heat of combustion per ton of coal and the amount of coal consumed. The energy output can be calculated using the amount of steam generated and the specific enthalpy of steam.

Explanation:

The efficiency of a coal plant can be calculated using the formula:

Efficiency = (Energy output / Energy input) * 100

To calculate the energy input, we can use the heat of combustion per ton of coal and the amount of coal consumed. The heat produced by combustion of a ton of coal is determined using a bomb calorimeter. Using the given information:

Heat capacity of calorimeter (C) = 21.6 kJ/°C
Temperature increase (ΔT) = 1.48 °C
Mass of coal burned (m) = 2.000 × 10³ pounds

We can calculate the energy input:

Energy input = (C * ΔT * m) / 1000

Substituting the given values:

Energy input = (21.6 kJ/°C * 1.48 °C * 2.000 × 10³ pounds) / 1000

To calculate the energy output, we can use the amount of steam generated. The energy output is given by:

Energy output = (Mass of steam * specific enthalpy of steam) - (Mass of water * specific enthalpy of water)

Using the given information:

Mass of steam = 6,400,000 lb.
Specific enthalpy of steam = Enthalpy at 520°F - Enthalpy at 200°F
Enthalpy at 520°F = Enthalpy of superheated steam at 520°F - Enthalpy of water at 520°F
Enthalpy at 200°F = Enthalpy of superheated steam at 200°F - Enthalpy of water at 200°F

We can calculate the energy output:

Energy output = (6,400,000 lb. * (Enthalpy at 520°F - Enthalpy at 200°F)) - (6,400,000 lb. * (Enthalpy of water at 520°F - Enthalpy of water at 200°F))

Finally, we can calculate the boiler efficiency:

Boiler efficiency = (Energy output / Energy input) * 100

Substituting the calculated energy input and energy output:

Boiler efficiency = (Energy output / ((21.6 kJ/°C * 1.48 °C * 2.000 × 10³ pounds) / 1000)) * 100

Calculating the value will give the efficiency of the coal plant.