Assignment 2

CE 115

1. Batch reactors are used by environmental engineers to treat hazardous waste. Batch reactors are essentially tanks in which contaminated liquid is treated. Contaminated liquid is placed in the tank and mixed with a reactant that, over time, combines with the waste, reducing its concentration and making the liquid less hazardous. After some time, the treated waste is removed.

The concentration of waste, C (mass contaminant per unit volume of liquid), within batch reactors can be modeled as a function of time by an exponential decay function:

C(t) = C₀e^-kt

where C is the concentration at some time t after mixing, C₀ is the initial concentration at t = 0, and k is the decay constant. The the value of the decay constant depends on many things, including the type of waste, the type of reactant, and the temperature of the reactor. Given C₀ = 100 milligrams/Liter and k = 0.2 days^-1, use Excel to complete the following:

1. Find the concentration of a hazardous waste at 5, 10, 25, and 50 days given C₀ = 100 milligrams/Liter and k = 0.2 days^-1.

2. When does the concentration in the reactor reach half its original value? The time at which this happens is known as the half-life.

3. Plot C versus t for a period of 50 days. Use an X-Y plot, making sure to fully label the axes and provide a title. Use enough "points" on your plot to make the curve smooth.

Here is how to format your Excel worksheet (and homeworks in general - you will be graded on these points):

Overall, be NEAT and ORGANIZED.

Start with a problem statement, that clearly and completely defines the problem to be solved. Present the given values, and state what is to be found.

Put given values, constants, parameters in dedicated locations (this makes it easy to change the values). Make sure that they are well-labeled, and include units wherever appropriate.

Put headers on columns of tables, make sure units are included.

Pay attention to significant figures.

In Excel, use absolute and relative cell references where appropriate.

Show calculations using text boxes - when the sheets are printed it is impossible to see the formulas in the cells. Make it clear to others the steps in your solution.

Put a title on graphs, label both axes, and show units.

Make sure answer(s) are clearly identified.