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Chapter 1: Problem 74

Oil spreads on water to form a film about \(100 \mathrm{~nm}\) thick (two significant figures). How many square kilometers of ocean will be covered by the slick formed when one barrel of oil is spilled (1 barrel \(=31.5\) U.S. gal)?

Short Answer

Expert verified
Answer: The oil slick will cover approximately 1.19 square kilometers of the ocean's surface.

Step by step solution

01

Write down the given information

The thickness of the oil film is \(100 \mathrm{~nm}\) (nanometers), and the volume of one barrel of oil is \(31.5\) U.S. gallons. First of all, we need to convert these values into meters and cubic meters, respectively.
02

Convert units

1 nanometer = \(10^{-9}\) meters. So, the thickness of the oil slick in meters is: \(100 \mathrm{~nm} = 100 \times 10^{-9} \mathrm{~m} = 1 \times 10^{-7} \mathrm{~m}\) 1 U.S. gallon is equal to \(3.78541 \times 10^{-3}\) cubic meters. So, the volume of one barrel of oil in cubic meters is: \(31.5 \mathrm{~gal} = 31.5 \times 3.78541 \times 10^{-3} \mathrm{~m^3} = 0.119 \mathrm{~m^3}\)
03

Find the surface area

Let the surface area of the ocean covered by the oil slick be A. Since volume is equal to area multiplied by thickness (height) of the oil slick, we can find A using the following equation: \(Volume = Area \times Thickness\) Substitute the given values and solve for A: \(0.119 \mathrm{~m^3} = A \times 1 \times 10^{-7} \mathrm{~m}\) \(A = \frac{0.119}{1 \times 10^{-7}} \mathrm{~m^2} = 1.19 \times 10^{6} \mathrm{~m^2}\)
04

Convert the surface area to square kilometers

1 square meter is equal to \(10^{-6}\) square kilometers. So, the surface area A in square kilometers is: \(1.19 \times 10^{6} \mathrm{~m^2} = 1.19 \times 10^{6} \times 10^{-6} \mathrm{~km^2} = 1.19 \mathrm{~km^2}\) The oil slick formed when one barrel of oil is spilled will cover approximately \(1.19 \mathrm{~km^2}\) of the ocean's surface.

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