1. A lake contains V = 3 * 10 m of water, and is fed by a river discharging Qupstream = 12 * 10 3 m year of water into the lake. An upstream factory pollutes this river with a concentration Criver 3 = 8.0 of the pollutant. Evaporation across the surface takes away Qevaporation = 3 * 10. mg L C. m 9 * 104 of water year = 0.15 year of water. Assume that the pollutant does not evaporate. Qdownstream exits the lake to the downstream stretch of the river. Inside the lake the pollutant decays with rate constant k (1st order elementary reaction). Assume that the volume of water in the lake is at steady state and that the lake is well-mixed. Follow the steps in the sub-questions (a-c) below to determine the steady state concentration of the pollutant in the downstream part of the river (i.e. determine Cdownstream, concentration of pollutant that is flowing out of the lake). a. Write the differential mass balance for the pollutant in the lake. b. Apply the steady state assumption and simplify the equation if necessary by crossing out any irrelevant terms. Solve for Cdownstream- river Qupstream VCK Q 3 Evaporation m year D Q downstream C downstream