Conceptual Physics

13.2 - Density

Density: Mass per unit volume.

Density í to be precise, mass densityí equals mass divided by volume. The Greek letterȡ (rho, pronounced “roe”) represents density. The SI unit for density is the kilogram per cubic meter. The gram per cubic centimeter is also a common unit, useful in part because the density of water is close to one gram per cubic centimeter. Liquids and solids retain a fairly constant density. It requires a great deal of force to compress water or a piece of clay into a more compact form. A given mass of liquid will change shape in order to conform to the shape of the container you pour it into, but its volume will remain nearly constant over a great variety of conditions. In contrast, the volume of a sample of gas changes readily, which means its density changes easily, as well. For example, when you pump a stroke of air into a bicycle tire, the volume of air in the pump cylinder is reduced to “squeeze” it into the tire, increasing the air's density. Much larger changes can be accomplished using larger increases in pressure. Machinery compresses the air fed into a scuba diving tank, causing its contents to be at a density on the order of 200 times greater than the density of the atmosphere you breathe. Before a diver breathes this air, its density (and pressure) are reduced. It would be lethal at the pressure maintained in the tank. The density of an object can vary at different points based on its composition. A precise way to state the definition of density is ǻm/ǻV: The mass of a small volume of material is measured to establish its local density. However, unless otherwise stated, we will assume that the substances we deal with have uniform density, the same density at all points. This means that the density can be established by dividing the total mass by the total volume. The table on the right shows the densities of various materials. Their densities are given at0°C and one standard atmosphere of pressure (the density of the air around you can vary, depending on atmospheric conditions). Exceptions to this are the super-dense neutron star, which has no temperature in the ordinary sense, and liquid water, whose density is given at 4°C, the temperature at which it is the greatest. We also supply some common equivalents for water, for instance relating a liter of water to its mass. The concept of specific gravity provides a useful tool for understanding and comparing various materials’ densities. Specific gravity divides the density of one material by that of a reference material, usually water at 4°C. For instance, if a material has a specific gravity of two, it is twice as dense as water.

Density

Ratio of mass to volume

ȡ = m/V

ȡ = density

m = mass

V = volume

Units: kg/m^3

Density of various substances

For water at 4º C:

·1 liter has mass of 1 kg

·1 cm^3 has mass of 1 g