# How do density and volume vary?

## Density and volume

### volume

The space that an object occupies is called volume.

The basic unit of volume is the cubic meter (m^{3}). However, 1 cubic meter is quite a large volume for the everyday work of physicists, so often smaller and more convenient units are used, as shown in the following figures:

Cubic meter (m^{3}) | Liter (l) | Cubic centimeters or milliliters (cm ^{3} or ml) |
---|---|---|

1 cubic meter (m^{3}) is the volume of a cube with an edge length of 1 m | 1 liter corresponds to the volume of 1 cubic decimeter (dm^{3}) | 1 cubic centimeter corresponds to the volume of a cube with an edge length of 1 cm |

1 cubic meter (m^{3}) = 1000 liters (l) | 1 liter (l) = 1000 cubic centimeters (cm^{3}) = 1000 milliliters (ml) | 1 cubic centimeter = 1 milliliter |

### density

Is lead heavier than water? Not necessarily! It depends on how the amounts of lead and water are compared. Because lead has a higher density than water and so more kilograms are "packed" in each cubic meter of lead than in one cubic meter of water.

The density of a material is calculated as follows:

$ \ mathrm {Density \ = \ \ frac {\ Large mass} {\ Large volume}} $

In the case of water, this means the following:

- 1000 kg of water takes up a volume of 1 m
^{3}a, - 2000 kg of water have a volume of 2 m
^{3}, - 3000 kg of water have a volume of 3 m
^{3}etc.

If you look at these values, you can easily see that the density of water is 1000 kg / m^{3} amounts.

If the mass in grams (g) and the volume in cubic centimeters (cm^{3}) are measured, it is easier to specify the density in g / cm³. The conversion to kg / m3 is easy:

$ \ mathrm {1 \ g / cm ^ {3} \ = \ 1000 \ kg / m ^ {3}} $

The density of the water is 1 g / cm^{3}. This seemingly simple value is no coincidence. The kilogram (1000 g) was originally thought to be the mass of 1000 cm^{3} Water (pure and at 4 ° C) defined. However, small errors crept in during the early measurements, so that this is no longer used as a definition of the kilogram.

material | density kg / m ^{3} | density g / cm ^{3} | material | density kg / m ^{3} | density g / cm ^{3} |
---|---|---|---|---|---|

air | 1,3 | 0,0013 | granite | 2700 | 2,7 |

Expanded polystyrene | 14 | 0,014 | aluminum | 2700 | 2,7 |

Beech wood | 750 | 0,75 | stainless steel | 7800 | 7,8 |

petrol | 800 | 0,80 | copper | 8900 | 8,9 |

Ice (0 ° C) | 920 | 0,92 | lead | 11.400 | 11,4 |

Polyethylene | 950 | 0,95 | mercury | 13.600 | 13,6 |

Water (4 ° C) | 1000 | 1,0 | gold | 19.300 | 19,3 |

concrete | 2400 | 2,4 | platinum | 21.500 | 21,5 |

Glass (varies) | 2500 | 2,5 | osmium | 22.600 | 22,6 |

### Calculate the density

The equation that connects density, mass and volume can be represented with symbols:

$ \ rho \ = \ \ frac {\ Large m} {\ Large V} $

$ \ rho $ = density, *m* = Mass and *V* = Volume

This formula can be changed:

$ \ mathrm {V \ = \ \ frac {\ Large m} {\ Large \ rho}} $

and

$ \ mathrm {m \ = \ V \ \ cdot \ \ rho} $

This is useful when you know the density but you want to calculate the volume or mass. On the right is one way how to find all three equations. Example:

Use the table above and calculate the mass of steel if it takes up the same volume as 5400 kg of aluminum.

First you calculate the volume of 5400 kg aluminum. Density of aluminum according to the table: 2700 kg / m^{3}, the mass is known: 5400 kg, and the volume should be calculated. In order to:

$ \ mathrm {V \ = \ \ frac {\ Large m} {\ Large \ rho} \ = \ \ mathrm {\ frac {\ Large {5400 \ kg}} {\ Large {2700 \ kg / m ^ 3} } \ = \ 2 \ m ^ 3}} $

So we want to know how much mass 2 m have^{3} Steel? Density of steel according to the table: 7800 kg / m^{3}, the volume is known: 2 m^{3}, and the mass should be calculated. In order to:

$ m \ = \ V \ rho \ = \ \ mathrm {7800 \ kg / m ^ 3 \ \ cdot \ 2 \ m ^ 3 \ = \ 15,600 \ kg} $

The mass of 2 m^{3} So steel is 15,600 kg!

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