U4735 Environmental Science for Policy Makers–Recitation. 1. Problem Set 5,
Solutions. 1. (13 points) Let's assume that a spherical cow has a radius of 100 cm
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U4735 Environmental Science for Policy Makers–Recitation
Problem Set 5, Solutions 1. (13 points) Let’s assume that a spherical cow has a radius of 100 cm and a boot has a radius of 5 cm. Then the number of boots that can be made from one cow is: 2 4πRcow 1002 cm2 cow−1 boots = 2 −1 = 400 2 2 4πRboot cow 5 cm boot For the second part we start with our result from the first part and multiply through such that the units of our final answer are boots. Information of the area of Antarctica can be found in the index of Spherical Cow. boots 10 cows 104 m2 7 400 × + .013475 × 0.149 × 1014 m2 × 2.9 × 10 acres × 2 cow 400 m 2.47 acres
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= 1 × 1012 boots 2. (25 points) (a) There are many ways to do this, here is one. First draw a line of best fit on the graph. This can be done by eye using a ruler. Next, read a set of points off the graph (any two that are well-spaced will do): c(0) = 104 , c(7000) = 102 . find their natural logarithms, using the change of base formula or by direct computation: ln c(0) =
(b) The formula for the concentration as a function of time is: c(t) = 104 e−0.00066t . We can check this by performing two calculations. c(0) = 104 e−0.00066×0 = 104 c(9000) = 104 e−0.00066×9000 = 26 Referring back to the graph, both of these are approximately correct (although we could have chosen others) thus the rate constant must be appoximately correct too.
U4735 Environmental Science for Policy Makers–Recitation
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3. (22 points) Exercise 1. Recall from class that the residence time is the stock divided by the flux in or out. Solving this equation for the stock we find: M =T ×F In this problem we are told that Fin = 7 cows/year and the residence time T is 6 years. Thus the stock is 7 × 6 = 42 cows. Exercise 2. (a) The stock in this problem is 100 students, the flux out, equal to the flux in, is 25 students/year, and thus the residence time is 100/25 = 4 years. (b) We have to be a bit more careful here. The stock, in this case is 100 − 5 = 95 students and the flux out of program of these 95 students is 20 students/year who graduate. Thus the residence time is 95/20 = 4.75 years.
