Density
Introduction
Density is the ratio of a material's mass to the volume of space it occupies.
The variable we are using to represent density, ρ, is the Greek letter rho, the equivalent of 'r'.
The usual units of density are kg/m³ or g/cm³.
Here is a review of the concept of volume.
If you need to learn how to do unit conversions of volumes, read Unit Conversions B.
The density of water is 1.00 g/cm3. Nice round number, isn't it? In fact, that's not a coincidence. The gram and kilogram were defined so that the density of water (at 4°C, at which water is its most dense) would work out to be 1.00 g/cm3. (The meter was defined in 1793 so it was 1/10,000,000th the distance from Earth's equator to the North Pole.)
The following table lists the densities of a variety of materials. Stuff that is gaseous (at standard temperature and pressure, 20°C and 1 atmosphere) are listed in red; liquids are green and solids are blue.
| density | ||
| material | g/cm³ | kg/m³ |
| hydrogen (STP) | 0.0000899 | 0.0899 |
| helium (STP) | 0.000179 | 0.179 |
| air (STP) | 0.00120 | 1.20 |
| wood | 0.35 to 0.9 | 350 to 900 |
| wood (yellow pine) | 0.550 | 550 |
| Saturn | 0.7 | 700 |
| gasoline | 0.737 | 737 |
| water ice | 0.917 | 917 |
| vegetable oil | 0.925 | 925 |
| water (4°C) | 1.00 | 1000 |
| ocean water | 1.026 | 1026 |
| table sugar | 1.587 | 1587 |
| table salt | 2.164 | 2164 |
| rocks | 2 to 3.5 | 2000 to 3500 |
| iron/steel | 7.9 | 7900 |
| copper | 8.94 | 8940 |
| mercury | 13.6 | 13600 |
| gold | 19.3 | 19300 |
| osmium | 22.6 | 22600 |
Activities & Practice
to do as you read
1. Which has largest volume, a kilogram of rock, a kilogram of styrofoam, or a kilogram of water?
2. Which has greatest density? A rock, styrofoam, or a cubic meter of water?
3. What is the density, in g/cm³, of the Earth? Its mass is 5.98x1024kg, and radius is 6378 km.
4. (a) What volume of air would have a mass of 1 kg? (b) If the air were in a cubical box, what would be the length of one edge of the box?
5. If you had a cubic inch of gold, what would be its mass?
Additional Activities & Practice
6. Let’s say your mass is 50 kg. Osmium metal has a density of 22.6 g/cm³.
(a) What volume (in m³) of Osmium metal would have the same mass as you?
(b) If you were to make a cube of Osmium with that volume, what would be the length of one edge?
7. Radius of a Uranium-238 nucleus is 7.4 femtometers, and its mass is 238 amu. (One femtometer = 1x10-15m; 1 amu = 1.66x10-27kg.) Calculate the density of a Uranium nucleus, in kg/m³ and g/cm³.
8. Let's say you could take the entire Sun and compress it down to the size of Earth. What would its density be? (The mass of the Sun is 1.99x1030 kg, and the radius of Earth is 6378 km.)
9. SPREADSHEET: Create a spreadsheet that has two input cells, the mass and radius of a sphere, and one calculated cell, the density of that sphere. Have the density in grams per cubic centimeter. Then, use your spreadsheet to calculate the density of the Earth (mass is 5.98E24 kg and radius is 6378 km). Also, use your spreadsheet to verify that your answer to question #8 is correct.