Fish and wildlife managers have determined that a sudden temperature increase greater than 5°C would be harmful to the marine ecosystem of a river. Warmer waters contain less dissolved oxygen and cause organisms in a river to increase their metabolism; if the temperature increase is sudden, the organisms do not have time to adapt to the new environment and likely will die. (Changes in river temperatures of five degrees and more due to seasonal temperature variations are common, but those temperature changes are gradual.) A proposed chemical plant plans to use river water for process cooling. The river flows at a rate of 15.0 m³/s at a temperature of 15°C, and a fraction of it will be diverted to the plant. Preliminary calculations reveal that the cooling water will remove 5.00 × 105 kJ/s of heat from the plant. A portion of the extracted water will evaporate from the plant into the atmosphere, and the remainder will be returned to the river at a temperature of 35°C. 

(a) Draw and completely label a flowchart of the process and prove that there is enough information available to calculate all of the unknown stream flow rates on the chart. 

(b) Estimate the fraction of the river flow that must be diverted to the plant and the percentage of the cooling water that evaporates. Assume that water has a constant heat capacity of 4.19 kJ/(kg•°C) and a heat of vaporization roughly that of water at the normal boiling point, and also assume that the specific enthalpy of the water vapor relative to liquid water at 15°C equals the heat of vaporization.

(c) Write (but don’t evaluate) an expression for the enthalpy change neglected by the assumption about the specific enthalpy of the steam.