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Chapter 1: Problem 3
Find the speed of light in miles per second.
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The volume of a sphere is equal to \(\frac{4}{3} \pi r^{3}\) where \(r\) is the radius of the sphere. Assume that the earth is spherical with a radius of \(3958.89\) miles. (This is the radius of a sphere with the same volume as the earth, which is flattened at the poles by about 30 miles.) Find the volume of the earth in cubic miles and in cubic meters. Using a value of \(\pi\) with at least six digits give the correct number of significant digits in your answer.
The value of an angle is given as \(31^{\circ}\). Find the measure of the angle in radians. Find the smallest and largest values that its sine and cosine might have and specify the sine and cosine to the appropriate number of digits.
Some elementary chemistry textbooks give the value of \(R\), the ideal gas constant, as \(0.08211 \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\) (a) Obtain the value of \(R\) in \(1 \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\) to five significant digits. (b) Calculate the pressure in atmospheres and in ( \(\mathrm{N} \mathrm{m}^{-2} \mathrm{~Pa}\) ) of a sample of an ideal gas with $$ n=0.13678 \mathrm{~mol}, \quad V=10.0001, \quad T=298.15 \mathrm{~K} . $$
The volume of a sphere is given by $$ V=\frac{4}{3} \pi r^{3} $$ where \(V\) is the volume and \(r\) is the radius. If a certain sphere has a radius given as \(0.005250 \mathrm{~m}\), find its volume, specifying it with the correct number of digits. Calculate the smallest and largest volumes that the sphere might have with the given information and check your first answer for the volume.
The hectare is a unit of land area defined to equal exactly \(10,000 \mathrm{~m}^{2}\), and the acre is a unit of land area defined so that 640 acre equals exactly one square mile. Find the number of square meters in \(1.000\) acre, and find the number of acres equivalent to \(1.000 \mathrm{ha}\).
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