African solar systems part 9: electricity generation

Electricity generation from heat is typically accomplished using a steam turbine - pressurized steam flows past a turbine causing the vanes of the turbine to rotate (and the steam to cool). This in turn drives an electric generator, and so the heat energy in the steam is converted to an electric current. Steam turbines follow various thermodynamic cycles, the most common of which is the Rankine cycle. There are two key aspects of turbines relevant to CSP electricity generation. The first is that the efficiency of steam turbines increases with input temperature. Therefore, in an ideal system with no heat loss one would want very, very hot steam to drive the turbine. Practically, since the heat losses from radiation, convection, and conduction all increase with temperature there is a balance in the overall system efficiency between the turbine efficiency and the transport and storage heat loss. Whether to further heat the steam before it enters the generator or increase the operating temperature of the steam above 250 $^\circ$ C throughout the whole system is a design decision for the system engineers.

A secondary concern for a generator is the erosion of the turbine blades caused by the steam itself. In particular, saturated versus superheated steam behave differently in a turbine. Saturated steam contains water vapor in equilibrium with the gaseous steam molecules. As steam passes through a turbine its temperature drops, which can result in condensation of water droplets. Since steam turbines operate at very high speeds, the presence of water droplets in the steam can cause damage to the turbine blades and parts (think about trying to fly through rain near the speed of sound). In general one wants to avoid condensation in a steam turbine.

The question

Steam enters a horizontal turbine with a temperature of 250 $^\circ$ C, absolute pressure of 400 kPa, and flow rate of 25 g/s. Steam exits the turbine at the same rate with no appreciable flow velocity and at atmospheric pressure. How much electrical power is produced by this turbine in Watts if the turbine uses the Rankine cycle and is 100 percent efficient? Round to the nearest thousand Watts.

You may use the steam calculator to figure this out.