Density and Specific Gravity

FIELDS OF STUDY: Classical Mechanics

ABSTRACT: Every object has mass, which measures the amount of matter contained in the object, and volume, which measures the three-dimensional space it takes up. The ratio of these values gives an object’s density. Comparing the density values of different objects yields specific gravity, a value that provides information about whether objects will float and the concentrations of various solutions.

PRINCIPAL TERMS

• gram: abbreviated g, a standard unit of mass in the International System of Units; derived from the kilogram (kg, thousands of grams), which is the base unit of mass.
• mass: the amount of matter contained in an object; it influences gravitation, motion, and—along with volume—density and specific gravity.
• slug: an alternate unit of mass, defined as a mass that accelerates one foot per second squared (1 ft/s²) when acted upon by one pound-force (lb_F).
• standard temperature and pressure (STP): a temperature of 273.15 kelvins (0 degrees Celsius or 32 degrees Fahrenheit) and pressure of 101.3 kilopascals (1 atmosphere); used in chemistry and physics to establish a standardized set of conditions for experimentation.
• volume: the space occupied by an object or substance, measured in cubic meters (m³); together with mass, it determines the density of an object and its specific gravity. Alternative units include liters (L) or cubic feet (ft³).
• weight: an object’s heaviness; the force imparted to an object by gravity acting on its mass, often measured in kilograms or pounds, although as a force, it should be given in newtons.

What Is Specific Gravity?

Density is a measure of how "tightly packed" the matter in a substance or object is. It is the ratio of an object’s mass relative to its volume. Mass quantifies how much matter is present in an object. Volume measures its three-dimensional space. Density (d) is calculated as the mass (m) divided by volume (V).

Mass can be measured in grams (g) or kilograms (kg), but slugs are an alternative unit of mass sometimes used in the United States and imperial measurement systems. One slug is 14,593 grams, or about 31 pounds. Volume is measured in cubic centimeters (cm³) when dealing with density, although liters or cubic inches are sometimes used.

Specific gravity describes the relationship between the density of a substance relative to that of some other substance—very often water. It is the ratio of two density values. It can be described as determining whether one substance will float in another. Specific gravity (SG) is computed as the density of the target object or substance (d_object) divided by the density (d_ref) of the reference object or substance. A substance will float if its density is less than that of the substance it is in; in other words, if its specific gravity is less than one. For example, ice in water has a specific gravity of about 0.9—its density is slightly less than that of liquid water, so it floats.

The density of some object or substance can also be found using its specific gravity and the density of its reference substance. In this case, the density of the object would be equal to the object’s specific gravity times the density of the referent.

It is possible to determine whether an object will float or sink if its mass and volume are known. Objects float when the buoyant force of the substance they are immersed in is enough to overcome their weight, that is, the force of gravity acting on their mass. The denser a substance is, the greater its buoyant force.

Standard Temperature and Pressure

By default, the specific gravity of solids and liquids is measured relative to the density of water,and gases relative to the density of air, with both reference substances at standard temperature and pressure (STP). STP is a temperature of 273.5 kelvins (0 degrees Celsius or 32 degrees Fahrenheit; the freezing point of water) and an atmospheric pressure of 101.3 kilopascals (roughly one atmosphere, the atmospheric pressure at sea level). STP is a way of standardizing the values against which densities and other values are compared. Solids, liquids, and gases all have different densities at different temperatures and pressures, with gases having the greatest variability. This is because gases, unlike solids and liquids, can change their volume. They will expand to fill whatever container they are in.

Sample Problem

Consider a solid ball. It has a mass of 60 grams. Its volume, measured using displacement, is 120 cubic centimeters. What is its specific gravity relative to freshwater (density 1 g/cm³), and will it float in it? Will it float in vegetable oil (density 0.92 g/cm³)? Will it float in a bowl of a mystery liquid with a mass of about 102 kilograms and a volume of 7,540 cubic centimeters?

Answer:

Begin by calculating the density of the ball in grams per cubic centimeter, using the formula for density:

d = m / V

d = 60 g / 120 cm³

d = 0.5 g/cm³

To get the specific gravity of the ball relative to freshwater, divide its density by the density of water:

SG_ball-water = d_ball / d_water

SG_ball-water = 0.5 g/cm³ ÷ 1 g/cm³

SG_ball-water = 0.5

To determine if the ball will float in water, ask whether its specific gravity is greater than or lower than a value of one—0.5 is less than 1.0, so it floats. For vegetable oil, repeat the process:

SG_ball-oil = d_ball / d_oil

SG_ball-oil= 0.5 g/cm³ ÷ 0.92 g/cm³

SG_ball-oil ≈ 0.54

The specific gravity relative to the oil is still less than 1, so it still floats (this makes intuitive sense, given that the density of water and vegetable oil is so similar: 1.0 g/cm³ versus 0.92 g/cm³).

For the mystery liquid, begin by calculating its density (remember to convert kilograms to grams before plugging in the given values):

d_? = m_? / V_?

d_? =102,000 g / 7,540 cm³

d_? = 13.53 g/cm³

Then use the same specific gravity equation as above:

SG_ball-? = d_ball / d_?

SG_ball-? = 0.5 g/cm³ ÷ 1.353 g/cm³

SG_ball-? ≈ 0.369

This very small value for specific gravity indicates that the ball would float nearly entirely on the surface of the liquid, which is extremely dense. The mystery liquid is modeled after mercury, the only metal that is a liquid at room temperature.

Practical Applications of Specific Gravity

Beyond the classroom application of determining whether a given object or substance will float in water, air, or another medium, specific gravity sees use in industry as a shorthand for the values of various solutions. This is possible due to the close relationship between density and specific gravity. With a variety of water-based solutions, specific gravity becomes an easy way to track the concentration of various substances in solution.

Consider a soft-drink factory, which uses a variety of syrups and other water-based solutions when mixing together drinks. In these situations, tables list various values of specific gravity for each substance relative to water and the corresponding concentration levels of that substance.

Bibliography

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"Q & A: What Is Specific Gravity?" Q & A: Physics Questions? Ask the Van. Dept. of Physics, U of Illinois at Urbana-Champaign, 22 Oct. 2007. Web. 26 June 2015.