Problem 67.

(a) One liter ( ) of oil is spilled onto a smooth lake. If the oil spreads out uniformly until it makes an oil slick just one molecule thick, with adjacent molecules just touching, estimate the diameter of the (roughly circular) oil slick. Assume the oil molecules have a diameter of .

(b) Recalculate for the Exxon Valdez oil spill (March 1989), in which 11 million gallons (42 million L) of crude oil coated Prince William Sound in Alaska.

Solution:

(a) To find the diameter of the oil slick we just need to write down the equation that the volume of the oil slick is equal to . The height of the oil slick is equal to the diameter of the molecule: .

Then the diameter of the oil slick can be found from the equation:

Then

(b) Now the volume is not but

Then using the same equations as in part (a) we obtain