Environmental Data Analysis BC ENV 3017

Homework 3 - answer key

Calibrations

1.) (12p) In your spreadhseet with the major anion standard data, determine the concentrations of the standards (the empty columns in your spreasdsheet).

a) Plot peakareas against ion concentration for Br^- and SO₄^2-. Add linear trendlines and their equation (peakarea = a*concentration + b) to the two graphs and print them out.

b) A sample was measured after the standards and yielded the following peakareas: 2,345,234 for Br^- and 115,678,254 for SO₄^2-.
Solve the two calibration equations from a) for the concentrations (i.e. concentration = (peakarea - b)/a) and use them to calculate the Br^- and SO₄^2- concentrations (in mg/L) for the sample.

See Excel file.

Back of the envelope calculations

2.) (10p) About what fraction of a cubic centimeter of rubber is worn off an automobile tire with each revolution of the wheel?

I assume a lifetime of a tire of 50,000 miles. The circumfence U of a tire can be calculated from its radius R:

U = 2*3.14 * R = 2 * 3.14 * 0.4 m = 2.5 m The number of revolutions of the tire = 30,000 miles / 2.5m * 1609 m /mile = 1.9*10⁷
I assume that over the lifetime of a tire 0.5 cm of rubber (D) are removed and that the width (W) of the tire is about 30 cm. The amount of rubber removed (V) then can be calculated by picturing the tire as a cyclinder wall: V = U * D * W = 2.5 m * 0.5 cm * 30 cm * 100 cm / m = 3750 cm³ is being removed from the tire:
Volume of rubber removed per revolution = 3750 cm³/ 1.9*10⁷ = 2 *10^-4 cm³.

Questions related to the readings

3.) (10p) Perform excercise 9 on page 126 of the book as repeated below. Please answer the questions and print the graphs. Here is the question as printed in the book:
The cars workbook contains information on car models from Consumer Reports, 2003-2008. Data in the workbook include the miles per gallon (MPG) of each car as well as the time to accelearate from 0-60, weight, horse-power, price, etc.
a) Open the Cars workbook from the chapter 03 folder and save it as Car Graphs.xlsx.
b) Create a scatter plot on a separate chart scheet of MPG (on the y-axis) versus horsepower (on the x-axis),
c) Label the poins that are highest in MPG as measured by the height above the average MPG for those with around the same horsepower. Label each of these points with the Model (make sure that you select only these points rather than all of these points - or else you'll wait a long time for all teh labels to be added to the plot). What do these cars have in common? (Hint: Each does not have just a traditional gasoline engine). Print your chart.
d) Create a bubble plot ona separate chart sheet with MPG on teh y-axis, horsepower on teh x axis and the size of each bubble determined by teh prize of the car. How do you interpret the graph?

See Excel file.