Answer:
To find the fraction of extraction steam flow (F_ex) and the specific pump work inputs, we can analyze the given power plant system with one closed Feedwater Heater (FWH). Let's break down the steps:
1. Determine the ideal Rankine cycle efficiency (η_ideal) based on the given conditions:
- Boiler exit temperature (T_boiler) = 900°C = 1173.15 K
- Condenser temperature (T_condenser) = 45°C = 318.15 K
η_ideal = 1 - (T_condenser / T_boiler)
2. Calculate the fraction of extraction steam flow (F_ex) using the ideal Rankine cycle efficiency:
η_ideal = (1 - (T_condenser / T_boiler)) = (1 - (318.15 K / 1173.15 K))
3. Calculate the specific pump work input for the pump that increases the extraction steam from 1 MPa to 5 MPa. This is the pump work to raise the pressure of the condensed extraction steam.
- Find the enthalpy difference between 1 MPa and 5 MPa for water at 200°C (h_5MPa - h_1MPa at 200°C).
- Calculate the specific pump work using the enthalpy difference.
4. Calculate the specific pump work input for the pump that increases the feedwater from 5 MPa at 45°C to the boiler temperature of 200°C.
- Find the enthalpy difference between 5 MPa at 45°C and 200°C (h_boiler at 200°C - h_5MPa at 45°C).
- Calculate the specific pump work using the enthalpy difference.
5. The fraction of extraction steam flow (F_ex) is the ratio of the specific pump work inputs:
F_ex = (Specific Pump Work to Raise Extraction Steam Pressure) / (Specific Pump Work to Raise Feedwater Pressure)
6. Calculate F_ex based on the specific pump work inputs obtained in steps 3 and 4.
Please note that you'll need access to steam tables or software that provides thermodynamic properties of water and steam at various temperatures and pressures to accurately calculate the specific enthalpy differences and pump work inputs. The specific values will depend on the specific properties of water and steam at the given conditions.