Steam enters the condenser of a steam power plant at 20 kPa and a quality of 95 % with a mass flow rate of 20,000 kg/h. It is to be cooled by water from a nearby river by circulating the water through the tubes within the condenser. To prevent thermal pollution, the river water is not allowed to experience a temperature rise above 10 ºC. If the steam is to leave the condenser as saturated liquid at 20 kPa, determine the mass flow rate of the cooling water required.

The steam enters the condenser as a vapor-liquid mix and exits as a saturated liquid. Specific enthalpies at inlet and outlet are given from a property table for saturated water:

Inlet

[tex]h_{in} = h_{f} + x\cdot (h_{fg})[/tex]

[tex]h_{in} = 251.42\,\frac{kJ}{kg} + 0.95\cdot (2357.5\,\frac{kJ}{kg} )[/tex]

[tex]h_{in} = 2373.17\,\frac{kJ}{kg}[/tex]

Outlet

[tex]h_{out} = h_{f}[/tex]

[tex]h_{out} = 251.42\,\frac{kJ}{kg}[/tex]

The heat transfer rate to the river is:

[tex]\dot Q_{out} = \dot m_{steam}\cdot (h_{in} - h_{out})[/tex]

[tex]\dot Q_{out} = (20000\,\frac{kg}{s} )\cdot (2373.17\,\frac{kJ}{kg}-251.42\,\frac{kJ}{kg} )[/tex]

[tex]\dot Q_{out} = 42.435\times 10^{6}\,W[/tex]

The mass flow rate of the cooling water is:

[tex]\dot m_{cooling} = \frac{\dot Q_{out}}{c_{p,w}\cdot \Delta T_{max}}[/tex]

[tex]\dot m_{cooling} = \frac{42.435\times 10^{6}\,W}{(4186\,\frac{J}{kg\cdot K} )\cdot (10\,K)}[/tex]

[tex]\cdot m_{cooling} = 1013.736\,\frac{kg}{s}[/tex]