Question

A flashed steam geothermal power plant is located where underground hot water is available as saturated liquid at 700 kPa. The well head pressure is 600 kPa. The
flashed steam enters a turbine at 500 kPa and expands to 15 kPa, when it is condensed. The flow rate from the well is 29.6 kg/s. determine the power produced in
kW.

Answer 1

Answer:

The power produced by the turbine is 74655.936 kW.

Explanation:

A turbine is a device that operates at steady-state. Let suppose that turbine does not have heat interactions with surroundings, as well as changes in potential and kinetic energies are neglictible. Power output can be determined by First Law of Thermodynamics:

$-\dot W_{out} + \dot m \cdot (h_{in}-h_{out}) = 0$

$\dot W_{out} = \dot m\cdot (h_{in}-h_{out})$

Let suppose that water enters as saturated vapor and exits as saturated liquid. Specific enthalpies are, respectively:

$h_{in} = 2748.1\,\frac{kJ}{kg}$

$h_{out} = 225.94\,\frac{kJ}{kg}$

The power produce by the turbine is:

$\dot W_{in} = \left(29.6\,\frac{kg}{s} \right)\cdot \left(2748.1\,\frac{kJ}{kg} - 225.94\,\frac{kJ}{kg} \right)$

$\dot W_{in} = 74655.936\,kW$