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Steam must be generated at 150°C for process heat in a food production facility. This is done in a combined heat and power system as extraction steam from the turbine. Assume the standard cycle has a turbine inlet of 3 MPa, 450°C and 60°C in the condenser. What pressure should be used for the extraction so there is a maximum of process heat at 150°C available and the least amount of turbine work lost?

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Answer:

To determine the extraction pressure that maximizes the process heat at 150°C and minimizes the turbine work lost in a combined heat and power system, you can use the concept of steam Rankine cycles. We'll need to find the extraction pressure (P_ex) that satisfies these conditions.

1. Start with the given conditions:

- Turbine inlet temperature (T_in) = 450°C = 723.15 K

- Condenser temperature (T_out) = 60°C = 333.15 K

- Desired process heat temperature (T_process) = 150°C = 423.15 K

2. Determine the ideal Rankine cycle efficiency (η_rankine) based on the given temperatures:

η_rankine = 1 - (T_out / T_in)

3. Calculate the ideal turbine work output per unit mass flow rate (W_turbine):

W_turbine = h_in - h_out

where h_in and h_out are the enthalpies at the turbine inlet and outlet, respectively.

4. Determine the enthalpy at the turbine inlet (h_in) using steam tables for the given conditions of 3 MPa and 450°C.

5. Calculate the enthalpy at the condenser outlet (h_out) using steam tables for the given conditions of 60°C.

6. Now, we need to find the extraction pressure (P_ex). The enthalpy of steam at this pressure should be equal to the enthalpy required for the process heat at 150°C. So,

h_process = h_ex

where h_process is the enthalpy at 150°C and h_ex is the enthalpy at the extraction pressure (P_ex).

7. Calculate h_process using the enthalpy of steam at 150°C.

8. Solve for P_ex by finding the pressure at which the enthalpy equals h_process.

9. The extraction pressure (P_ex) found in step 8 will be the pressure that maximizes the process heat at 150°C while minimizing turbine work losses.

Please note that you'll need access to steam tables or software that can provide thermodynamic properties of steam at various pressures and temperatures to perform these calculations accurately. The specific values will depend on the steam properties and your particular system configuration.

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