The central goal of this standard set is to be able to answer the simple question, Will an object sink or will it float? Students will learn that density is a physical property of a substance independent of how much of the substance is available, and they will be able to relate the property of density to the phenomenon of buoyancy. Archimedes, a Greek mathematician, is credited with first recognizing that different substances have different densities and that fluids exert a buoyant force on objects submerged in them. He came to this understanding while trying to determine what else was in a supposedly gold crown.

Archimedes came to a simple realization: water does not sink in water. That is, if one focuses on one drop of water in a container of water (and if one could keep the drop intact and distinct), the drop would not fall to the bottom of the container even though it has weight. The surrounding water must exert an upward buoyant force on the drop equal to the weight of the drop. The drop would fall if its weight were greater than the buoyant force supplied by the surrounding water. The drop would rise if it weighed less than the buoyant force. The surrounding water exerts an upward buoyant force on any volume within it equal to the weight of that volume of water. Understanding the nature of floating and sinking led Archimedes to realize that different substances have different densities—the key to determining whether the crown was gold or a fake.

Density is a property characteristic of the material itself and does not change whether the material is subdivided or the amount available is altered. Different substances have different densities, so knowing the density of a sample is useful in determining its composition. For example, the composition of Earth’s interior was first inferred to be different from the composition of rocks in the lithosphere because the density of lithospheric rocks is different from the average density of Earth.

The density of solids and liquids, the two condensed states of matter, does not vary much with changes in pressure or temperature. However, small differences in density within a liquid or gas may be caused by local heating and result in convection currents. Because gases are so compressible, their densities may vary over a wide range of values. That is why tables of measured values of density are found only for solids and liquids.

Most fluids (gases and liquids) are very poor conductors of heat. Normally, fluids expand when their temperature increases because of the more rapid motion of the constituent molecules. If a fluid is heated locally, the thermal energy is not conducted rapidly to other parts of the fluid; the region that is hotter expands, becoming less dense than the cooler surrounding fluid. The buoyant force supplied by the cooler surrounding fluid on the hotter expanded region is greater than the weight of the hotter region. This force causes the hotter, less dense region of fluid to be pushed up, a phenomenon known as “Hot air rises.”

A thorough understanding of density and buoyancy will be helpful in mastering the earth science standards in high school.