A 1 GW power plant is to be constructed on a Rankine cycle w

A 1 GW power plant is to be constructed on a Rankine cycle with water as the working fluid with thermal efficiency eta = 45%. A local river is used in the condensers. High temperature in the Rankine cycle is 600 degree C and condenser pressure gets down to 20 kPa. Calculate the rise in temperature of the river from intake to discharge.

Solution

Heat input = Work input / efficiency   = 10^9 / 0.45   = 2.2222 GW

Heat lost through condenser   = 2.2222 - 1   = 1.2222   GW

Heat lost through condenser = heat gained by water

1.2222 * 10^9    = mass flow rate * 4200 * (temperature difference)

mass flow rate of water = mean speed * area

please substitute mean speed and area of flow from figure, it is not clear enough in the photo.

291 * 10^3 / mass flow rate    = (temperature difference)