Chapter 10 Fluid Statics – Floating and Sinking
10.2 Density
Summary
- 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.
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.
DENSITY
Density is mass per unit volume.
In equation form, density is defined as ρ = mass / Volume
where the Greek letter ρ 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 kg / m3 representative values are given in Table 1. The metric system was originally devised so that water would have a density of 1 gram / cubic centimeter = 1 g/cm 3 equivalent to 1000 kg / m3 . 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 | ρ (103 kg/m3 or g/mL) | Substance | ρ (103 kg/m3 or g/mL) | Substance | ρ (103 kg/m3 or g/mL) |
|---|---|---|---|---|---|
| Solids | Liquids | Gases | |||
| Aluminum | 2.7 | Water (4ºC) | 1.000 | Air | 1.29 x 10-3 |
| Brass | 8.44 | Blood | 1.05 | Carbon dioxide | 1.29 x 10-3 |
| Copper (average) | 8.8 | Sea water | 1.025 | Carbon monoxide | 1.25 x 10-3 |
| 19.32 | Mercury | 13.6 | Hydrogen | 0.090 x 10-3 | |
| Iron or steel | 7.8 | Ethyl alcohol | 0.79 | Helium | 0.18 x 10-3 |
| Lead | 11.3 | Petrol | 0.68 | Methane | 0.72 x 10-3 |
| Polystyrene | 0.10 | Glycerin | 1.26 | Nitrogen | 1.25 x 10-3 |
| Tungsten | 19.30 | Olive oil | 0.92 | Nitrous oxide | 1.98 x 10-3 |
| Uranium | 18.70 | Oxygen | 1.43 x 10-3 | ||
| Concrete | 2.30–3.0 | Steam 100º C | 0.60 x 10-3 | ||
| Cork | 0.24 | ||||
| Glass, common (average) | 2.6 | ||||
| Granite | 2.7 | ||||
| Earth’s crust | 3.3 | ||||
| Wood | 0.3–0.9 | ||||
| Ice (0°C) | 0.917 | ||||
| Bone | 1.7–2.0 | ||||
| Table 1. Densities of Various Substances |
As you can see by examining the tables of density, the density of an object may help identify its composition. The density of gold, for example, is about 2.5 times the density of iron, which is about 2.5 times the density of aluminum. Density also reveals something about the phase of the matter and its substructure. Notice that the densities of liquids and solids are roughly comparable, consistent with the fact that their atoms are in close contact. The densities of gases are much less than those of liquids and solids, because the atoms in gases are separated by