47 Density
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Learning Objectives
- Define density.
- Calculate the mass of a reservoir from its density.
- Compare and contrast the densities of various substances.
Which weighs more, a ton of feathers or a ton of bricks? This old riddle plays with the distinction between mass and density. A ton is a ton, of course; but bricks have much greater density than feathers, and so we are tempted to think of them as heavier. (See (Figure).)
Density, as you will see, is an important characteristic of substances. It is crucial, for example, in determining whether an object sinks or floats in a fluid. Density is the mass per unit volume of a substance or object. In equation form, density is defined as
where the Greek letter \(\rho \) (rho) is the symbol for density, \(m\) is the mass, and \(V\) is the volume occupied by the substance.
Density is mass per unit volume.
where \(\rho \) is the symbol for density, \(m\) is the mass, and \(V\) is the volume occupied by the substance.
In the riddle regarding the feathers and bricks, the masses are the same, but the volume occupied by the feathers is much greater, since their density is much lower. The SI unit of density is \({\text{kg/m}}^{3}\), representative values are given in (Figure). The metric system was originally devised so that water would have a density of \(1\phantom{\rule{0.25em}{0ex}}{\text{g/cm}}^{3}\), equivalent to \({\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}{\text{kg/m}}^{3}\). Thus the basic mass unit, the kilogram, was first devised to be the mass of 1000 mL of water, which has a volume of 1000 cm3.
| Substance | \(\rho \left({\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}{\text{kg/m}}^{3}\phantom{\rule{0.25em}{0ex}}\text{or}\phantom{\rule{0.25em}{0ex}}\text{g/mL}\right)\) | Substance | \(\rho \left({\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}{\text{kg/m}}^{3}\phantom{\rule{0.25em}{0ex}}\text{or}\phantom{\rule{0.25em}{0ex}}\text{g/mL}\right)\) | Substance | \(\rho \left({\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}{\text{kg/m}}^{3}\phantom{\rule{0.25em}{0ex}}\text{or}\phantom{\rule{0.25em}{0ex}}\text{g/mL}\right)\) |
|---|---|---|---|---|---|
| Solids | Liquids | Gases | |||
| Aluminum | 2.7 | Water (4ºC) | 1.000 | Air | \(1\text{.}\text{29}×{\text{10}}^{-3}\) |
| Brass | 8.44 | Blood | 1.05 | Carbon dioxide | \(1\text{.}\text{98}×{\text{10}}^{-3}\) |
| Copper (average) | 8.8 | Sea water | 1.025 | Carbon monoxide | \(1\text{.}\text{25}×{\text{10}}^{-3}\) |
| Gold | 19.32 | Mercury | 13.6 | Hydrogen | \(0\text{.}\text{090}×{\text{10}}^{-3}\) |
| Iron or steel | 7.8 | Ethyl alcohol | 0.79 | Helium | \(0\text{.}\text{18}×{\text{10}}^{-3}\) |
| Lead | 11.3 | Petrol | 0.68 | Methane | \(0\text{.}\text{72}×{\text{10}}^{-3}\) |
| Polystyrene | 0.10 | Glycerin | 1.26 | Nitrogen | \(1\text{.}\text{25}×{\text{10}}^{-3}\) |
| Tungsten | 19.30 | Olive oil | 0.92 | Nitrous oxide | \(1\text{.}\text{98}×{\text{10}}^{-3}\) |
| Uranium | 18.70 | Oxygen | \(1\text{.}\text{43}×{\text{10}}^{-3}\) | ||
| Concre