\(\def \u#1{\,\mathrm{#1}}\) \(\def \abs#1{\left|#1\right|}\) \(\def \ast{*}\) \(\def \deg{^{\circ}}\) \(\def \ten#1{\times 10^{#1}}\) \(\def \redcancel#1{{\color{red}\cancel{#1}}}\) \(\def \BLUE#1{{\color{blue} #1}}\) \(\def \RED#1{{\color{red} #1}}\) \(\def \PURPLE#1{{\color{purple} #1}}\) \(\def \th#1,#2{#1,\!#2}\) \(\def \lshift#1#2{\underset{\Leftarrow\atop{#2}}#1}}\) \(\def \rshift#1#2{\underset{\Rightarrow\atop{#2}}#1}}\) \(\def \dotspot{{\color{lightgray}{\circ}}}\)

Density

The mass density (or just density, in this chapter) of an object is the amount of mass an object has divided by its volume:

Density is a property of the material an object is made of, not its size. For example, if we have one box which is $5\u{kg}$ and $0.0015\u{m^3}$, and then we attach to it a second box of the same size and mass, the pair of boxes together have twice the mass ($10\u{kg}$) and twice the volume ($0.0030\u{m^3}$), but the density is the same:

$$\rho={5\u{kg}\over 0.0015\u{m^3}}={10\u{kg}\over 0.0030\u{m^3}}=3,\!330\u{kg/m^3}$$ Notice that the units of density are kilograms per cubic meter, or $\u{kg/m^3}$. Now, a cubic meter is huge: think of a cube built out of metersticks. A cubic meter of a solid or a liquid is thus pretty massive, and densities of 100's or 1000's of kilograms per cubic meter are quite common:

• Wood has a density around $500\u{kg/m^3}$
• Stone around $1500\u{kg/m^3}$
• Water has a density of $1000\u{kg/m^3}$: in fact, the kilogram was originally defined so that this would be true.

Some things, like pillows or marshmallows, may have a density which can be increased easily under compression. And gases take on whatever density is required to fill the container they’re in. The air around you has a density of $1.2\u{kg/m^3}$, but the density is larger in a balloon or a tire, for instance.

The density of all objects depends at least partly on temperature. Usually (but not always) warming up an object will cause an object to expand, which decreases its density.