When energy is added to matter its temperature will rise. The temperature rise will depend on the mass which in turn depends on its density.

Density describes how closely packed the particles are in a solid, liquid or gas.

All matter contains particles. The difference between the different states of matter is how the particles are arranged:

- in a solid - particles are tightly packed in a regular structure
- in a liquid - particles are tightly packed but free to move past each other
- in a gas - particles are spread out and move randomly

There is little difference between the density of a liquid and its corresponding solid, eg water and ice. This is because the particles are tightly packed in both states. The same number of particles in a gas would spread further apart compared to in the liquid or solid states. The same mass takes up a bigger volume - this means the gas is less dense.

Density also depends on the material. A piece of iron with the same dimensions as a piece of aluminium will be heavier because the atoms are more closely packed.

Scientists can measure how tightly packed the particles are by measuring the mass of a certain volume of the material, for example, one metre cubed.

Material | Density in kilograms per cubic centimetre (cm^{3}) |
---|---|

Iron | 7,800 |

Ice | 980 |

Water | 1,000 |

Air | 1.2 |

Density can be calculated using the equation:

\[density = \frac{mass}{volume}\]

\[p = \frac{m}{V}\]

This is when:

- density (
*p*) is measured in kilograms per metre cubed (kg/m^{3}) - mass (
*m*) is measured in kilograms (kg) - volume (
*V*) is measured in metres cubed (m^{3})

What is the density of a material if 0.45 metres cubed (m^{3}) of it has a mass of 0.2 kg?

\[p = \frac{m}{V}\]

\[p = \frac{0.2}{0.45}\]

\[p = 0.44~kg/m^3\]

- Question
What is the density of a material if 4 metres cubed (m

^{3}) of it has a mass of 2,200 kg?\[p = \frac{m}{V}\]

\[p = \frac{2,200}{4}\]

\[p = 550~kg/m^3\]

Although the standard unit for mass is kilograms (kg) and for volume is metres cubed (m^{3}), in many laboratory situations the norm is finding the mass in grams (g) and volume in centimetres cubed (cm^{3}).

Calculating density using grams and centimetres cubed would give a density unit of grams per centimetre cubed (g/cm^{3}).

- Question
What is the density of a material if 15 cm

^{3}of it has a mass of 30 g?\[p = \frac{m}{V}\]

\[p = \frac{30}{15}\]

\[p = 2~g/cm^3\]

1 g/cm^{3} is equal to 1,000 kg/m^{3}

- To convert from kg/m
^{3}to g/cm^{3}, divide by 1,000. - To convert from g/cm
^{3}to kg/m^{3}, multiply by 1,000.

Aluminium has a density of 2.7 g/cm^{3}, or 2,700 kg/m^{3}. Lead has a density of 11.6 g/cm^{3}, or 11,600 kg/m^{3}.

Iron has a density of 7.9 g/cm^{3}. What is this in kg/m^{3}?

7.9 multiplied by 1,000 gives 7,900 kg/m^{3}.

- Question
What is the density of an object in kg/m

^{3}if it is 22.61 g/cm^{3}?22.61 multiplied by 1,000 would give 22,610 kg/m

^{3}.