How to Solve for Specific Gravity

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"Specific gravity" is, on its face, a somewhat misleading term. It has little to do with gravity, which is obviously an indispensable concept in a range of physics problems and applications. Instead, it relates to the amount of matter (mass) of a specific substance within a given volume, set against the standard of perhaps the most vital and ubiquitous substance known to humankind – water.

While specific gravity doesn't explicitly use the value of Earth's gravity (which is often referred to as a force, but in fact has units of acceleration in physics – 9.8 meters per second per second at the surface of the planet, to be exact), gravity is an indirect consideration because things that are "heavier" have higher specific-gravity values than things that are "lighter." But what do words like "heavy" and "light" even mean in the formal sense? Well, that's what physics is for.

Density: Definition

First, specific gravity is very closely related to density, and the terms are often used interchangeably. As with a lot of concepts in the world of science, this is generally acceptable, but when considering the effect that small changes in meaning and quantities can have on the physical world, it's not a negligible difference.

Density is simply mass divided by volume, full stop. If you're given a value for the mass of something and you know how much space it takes up, you can immediately calculate its density. (Even here, nettlesome issues can arise. This calculation assumes that the material has uniform compositions throughout its mass and volume and that its density is therefore uniform. Otherwise, all you're calculating is an average density, which may or may not be okay for the requirements of the problem at hand.)

Of course, it helps to have a number that makes sense when you're through with your calculation – one that is commonly used. So if you have the mass of something in ounces and the volume in microliters, say, dividing mass by volume to get density leaves you with very awkward units of ounces per microliters. Instead, aim for one of the common units, like g/ml, or grams per milliliter (which is the same thing as g/cm3, or grams per cubic centimeter). By original definition, 1 ml of pure water has a mass of very, very close to 1 g, so close that the density of water is almost always simply rounded to "exactly" 1 for everyday purposes; this makes g/ml a particularly handy unit, and it comes into play in specific gravity.

Factors Affecting Density

The density of substances is rarely constant. This is especially true of liquids and gases (that is, fluids), which are more sensitive to changes in temperature than solids. Liquids and gases also accommodate the addition of extra mass with no change in volume in a way that solids cannot.

For example, water exists in its liquid state between 0 degrees Celsius and 100 C. As it warms from the lower end of this range to the higher end, it expands. That is, the same amount of mass consumes more and more volume with rising temperature. As a result, water becomes less dense with increasing temperature.

Another way in which liquids undergo density changes is the addition of particles that dissolve in the liquid, called solutes. For example, fresh water contains very little salt (sodium chloride), whereas sea water famously contains a great deal of it. When salt is added to water, its mass increases while its volume, for all practical purposes, does not. This means that sea water is more dense than fresh water, and that sea water with especially high salinity (salt content) is more dense than typical sea water or sea water with relatively little salt, such as that near the mouth of a major freshwater river.

The implication of these differences is that, because less-dense materials exert a lower amount of downward pressure than more-dense materials, water often forms layers on the basis of differences in temperature, salinity or some combination. For example, water already near the surface of water will be heated by the sun more than deeper water will, making that surface water less dense and therefore even more likely to keep atop the layers of water beneath.

Specific Gravity: Definition

Specific gravity units are not the same as for density, which is mass per unit volume. This is because the specific gravity formula is slightly different: It is the density of the material under study divided by the density of water. More formally, the specific gravity equation is:

(mass of material ÷ volume of material) ÷ (mass of water ÷ volume of water)

If the same container is used to measure both the volume of the water and the volume of the substance, then these volumes can be treated as the same and factored out of the above equation, leaving the formula for specific gravity as:

(mass of material ÷ mass of water)

Because density divided by density and mass divided by mass are both unitless, specific gravity is also unitless. It is simply a number.

The mass of water in a container of fixed water will change with the water's temperature, which in most cases is close to the temperature of the room it is in if it sits for a time. Recall that the density of water drops with temperature as water expands. Specifically, water at a temperature of 10 C has a density of 0.9997 g/ml, while water at 20 C has a density of 0.9982 g/ml. Water at 30 C has a density of 0.9956 g/ml. These differences of tenths of a percent may seem trivial on the surface, but when you want to determine the density of a substance with great precision, you really have to resort to using specific gravity.

Related Units and Terms

Specific volume, denoted by v (small "v,"and not to be confused with velocity; context should be of aid here), is a term applied to gases, and it is the volume of the gas divided by its mass, or V/m. This is merely the reciprocal of the gas's density. The units here are usually m3/kg rather than ml/g, the latter being what you might expect given the most common unit of density. Why might this be? Well, consider the nature of gases: They are very diffuse, and collecting a significant mass of it is not easy unless one is able to deal in larger volumes.

In addition, the concept of buoyancy is related to density. In a previous section, it was noted that more-dense objects exert more downward pressure than do less-dense objects. More generally, this implies that an object placed in water will sink if its density is greater than that of water but float if its density is less than that of water. How would you explain the behavior of ice cubes, based only on what you have read here?

In any event, buoyant force is the force of a fluid on an object immersed in that fluid that counters the force of gravity compelling the object to sink. The more dense a fluid, the greater the buoyant force it will exert on a given object, reflected in that object's lower likelihood of sinking.

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