Answer:
To find the cycle efficiency of a Rankine cycle with an actual turbine, you can follow these steps:
1. Start with the given conditions:
- Boiler pressure (P_boiler) = 3 MPa
- Boiler superheat temperature (T_boiler) = 500°C = 773.15 K
- Condenser temperature (T_condenser) = 100°C = 373.15 K
- Turbine exit state: Saturated vapor at 100°C
2. Determine the efficiency of the ideal Rankine cycle (η_ideal) using the given temperature values:
η_ideal = 1 - (T_condenser / T_boiler)
3. Calculate the ideal turbine work output per unit mass flow rate (W_turbine_ideal):
W_turbine_ideal = h_boiler - h_condenser
where h_boiler and h_condenser are the enthalpies at the boiler and condenser states, respectively, based on the given temperatures and pressures.
4. Determine the actual turbine work output per unit mass flow rate (W_turbine_actual) based on the given exit state of the turbine (saturated vapor at 100°C). You'll need to find the enthalpy of saturated vapor at 100°C and 3 MPa.
5. Calculate the cycle efficiency with the actual turbine:
η_actual = W_turbine_actual / Q_in
where Q_in is the heat input to the cycle, which is equal to the ideal turbine work output (W_turbine_ideal) since all other components are ideal.
6. Finally, calculate η_actual using the values you've obtained in steps 2, 4, and 5.
Keep in mind that in step 4, finding the enthalpy of saturated vapor at 100°C and 3 MPa requires consulting steam tables or using appropriate thermodynamic software. Once you have that value, you can calculate the actual turbine work output and then the cycle efficiency with the actual turbine. The actual turbine efficiency may be less than the ideal efficiency due to the turbine's departure from ideal behavior.