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Chapter 1: Problem 27
A typical sugar cube has an edge length of \(1 \mathrm{~cm} .\) If you had a cubical box that contained 1 mole of sugar cubes, what would its edge length be?
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(a) In track meets both 100 yards and 100 meters are used as distances for dashes. Which is longer? By how many meters is it longer? By how many feet? (b) Track and field records are kept for the mile and the so-called metric mile \((1500 \mathrm{me}-\) ters). Compare these distances.
Astronomical distances are so large compared to terrestrial ones that much larger units of length are used for easy comprehension of the relative distances of astronomical objects. An astronomical unit \((\mathrm{AU})\) is equal to the average distance from Earth to the Sun, \(1.50 \times 10^{8} \mathrm{~km}\). A parsec (pc) is the distance at which 1 AU would subtend an angle of 1 second of arc. A light-year (ly) is the distance that light, traveling through a vacuum with a speed of \(3.00 \times 10^{5} \mathrm{~km} / \mathrm{s}\), would cover in 1 year. ( \(a\) ) Express the distance from Earth to the Sun in parsecs and in light-years. (b) Express a light-year and a parsec in kilometers. Although the light-year is much used in popular writing, the parsec is the unit preferred by astronomers.
A unit of area, often used in expressing areas of land, is the hectare, defined as \(10^{4} \mathrm{~m}^{2}\). An open-pit coal mine consumes 77 hectares of land, down to a depth of \(26 \mathrm{~m}\), each year. What volume of earth, in cubic kilometers, is removed in this time?
Porous rock through which groundwater can move is called an aquifer. The volume \(V\) of water that, in time \(t\), moves through a cross section of area \(A\) of the aquifer is given by $$ V / t=K A H / L $$ where \(H\) is the vertical drop of the aquifer over the horizontal distance \(L\); see Fig. \(1-5 .\) This relation is called Darcy's law. The quantity \(K\) is the hydraulic conductivity of the aquifer. What are the SI units of \(K ?\)
Enrico Fermi once pointed out that a standard lecture period \((50 \mathrm{~min})\) is close to 1 microcentury. How long is a microcentury in minutes, and what is the percentage difference from Fermi's approximation?
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