Question

Steam enters a steam turbine at 10 MPa and 600°C with a mass flow rate of 16 kg/s. The steam exits the turbine as saturated vapor at 10 kPa. Under steady state condition, the turbine generates 16.2 MW power. If the ambient temperature is 25°C, the rate of entropy generation in the turbine is _________ kW/K (round off to 2 decimal places).

Hint:

The rate of entropy generation is related to the change in entropy between the inlet and exit states and the mass flow rate.

Answer 1

Correct Answer: 21

Entropy change per unit mass of steam (before and after):
\[ \Delta s = s_{\text{exit}} - s_{\text{inlet}} \] From the given data: \[ s_{\text{inlet}} = 6.9028\ \text{kJ/(kg K)} \quad \text{(at 600°C, 10 MPa)} \] \[ s_{\text{exit}} = 8.1501\ \text{kJ/(kg K)} \quad \text{(at 10 kPa, saturated vapor)} \] Thus, the change in entropy per unit mass is:
\[ \Delta s = 8.1501 - 6.9028 = 1.2473\ \text{kJ/(kg K)} \] The rate of entropy generation (\( \dot{S}_{gen} \)) is given by:
\[ \dot{S}_{gen} = \dot{m} \Delta s \] where \( \dot{m} = 16\ \text{kg/s} \) is the mass flow rate. Substitute values:
\[ \dot{S}_{gen} = 16 \times 1.2473 = 19.96\ \text{kW/K} \] Thus, the rate of entropy generation in the turbine is approximately:
\[ \dot{S}_{gen} = 20.00\ \text{kW/K} \] Rounded to 2 decimals:
\[ \dot{S}_{gen} = 20.00\ \text{kW/K} \]