Volume is the amount of space occupied by
an object or a material. Volume is said to be a derived unit, since the
volume of an object can be known from other measurements. In order to
find the volume of a rectangular box, for example, one only needs to
know the length, width, and depth of the box. Then the volume can be
calculated from the formula, V = l · w · d.
The volume of most physical objects is a
function of two other factors: temperature and pressure. In general, the
volume of an object increases with an increase in temperature and
decreases with an increase in pressure. Some exceptions exist to this
general rule. For example, when water is heated from a temperature of
32°F (0°C) to 39°F (4°C), it decreases in volume. Above 39°F,
however, further heating of water results in an increase in volume that
is more characteristic of matter.
**Units
of volume**
The term unit volume refers to the volume
of "one something": one quart, one milliliter, or one cubic
inch, for example. Every measuring system that exists defines a unit
volume for that system. Then, when one speaks about the volume of an
object in that system, what he or she means is how many times that unit
volume is contained within the object. If the volume of a glass of water
is said to be 35.6 cubic inches, for example, what is meant is that 35.6
cubic inch unit volumes could be placed into that glass.
The units in which volume is measured
depend on a variety of factors, such as the system of measurement being
used and the type of material being measured. For example, volume in the
British system of measurement may be measured in barrels, bushels,
drams, gills, pecks, teaspoons, or other units. Each of these units may
have more than one meaning, depending on the material being measured.
For example, the precise size of a barrel ranges anywhere from 31 to 42
gallons, depending on federal and state statutes. The more standard
units used in the British system, however, are the cubic inch or cubic
foot and the gallon.
Variability in the basic units also exists.
For example, the quart differs in size depending on whether it is being
used to measure a liquid or dry volume and whether it is a measurement
made in the British or customary U.S. system. As an example, 1 customary
liquid quart is equivalent to 57.75 cubic inches, while 1 customary dry
quart is equivalent to 67.201 cubic inches. In contrast, 1 British quart
is equivalent to 69.354 cubic inches.
The basic unit of volume in the metric
system is the liter (abbreviated as L), although the cubic centimeter
(cc or cm^{3}) and milliliter (mL) are also widely used as units
for measuring volume. The fundamental relationship between units in the
two systems is given by the fact that 1U.S. liquid quart is equivalent
to 0.946 liter or, conversely, 1 liter is equivalent to 1.057 customary
liquid quarts.
**Words
to Know**
**British
system:** A system of
measurement long used in many parts of the world but now used commonly
only in the United States among the major nations of the world.
**Displacement
method:** A method for
determining the volume of an irregularly shaped solid object by placing
it in a measured amount of water or other liquid and noting the increase
in volume of the liquid.
**Metric
system:** A system of
measurement used by all scientists and in common practice by almost
every nation of the world.
**Unit
volume:** The basic size
of an object against which all other volumes are measured in a system.
**The
volume of solids**
The volumes of solids are relatively less
affected by pressure and temperature changes than are the volumes of
most liquids and all gases. For example, heating a liter of iron from
0°C to 100°C causes an increase in volume of less than 1 percent.
Heating a liter of water through the same temperature range causes an
increase in volume of less than 5 percent. But heating a liter of air
from 0°C to 100°C causes an increase in volume of nearly 140 percent.
The volume of a solid object can be
determined in one of two general ways, depending on whether or not a
mathematical formula can be written for the object. For example, the
volume of a cube can be determined if one knows the length of one side.
In such a case, V = s^{3}, or the volume of the cube is equal to
the cube of the length of any one side (all sides being equal in
length). The volume of a cylinder, on the other hand, is equal to the
product of the area of the base multiplied by the height of the
cylinder.
Many solid objects have irregular shapes
for which no mathematical formula exists. One way to find the volume of
such objects is to subdivide them into recognizable shapes for which
formulas do exist (such as many small cubes) and then approximate the
total volume by summing the volumes of individual sub-divisions. This
method of approximation can become exact by using calculus.
Another way is to calculate the volume by
water displacement, or the displacement of some other liquid. Suppose,
for example, that one wishes to calculate the volume of an irregularly
shaped piece of rock. One way to determine that volume is first to add
water to some volume-measuring instrument, such as a graduated cylinder.
The exact volume of water added to the cylinder is recorded. Then, the
object whose volume is to be determined is also added to the cylinder.
The water in the cylinder will rise by an amount equivalent to the
volume of the object. Thus, the final volume read on the cylinder less
the original volume is equal to the volume of the submerged object.
This method is applicable, of course, only
if the object is insoluble in water. If the object is soluble in water,
then another liquid, such as alcohol or cyclohexane, can be substituted
for the water.
**The
volume of liquids and gases**
Measuring the volume of a liquid is
relatively straightforward. Since liquids take the shape of the
container in which they are placed, a liquid whose volume is to be found
can simply be poured into a graduated container, that is, a container on
which some scale has been etched. Graduated cylinders of various sizes
ranging from 10 milliliters to 1 liter are commonly available in science
laboratories for measuring the volumes of liquids. Other devices, such
as pipettes and burettes (small measuring tubes), are available for
measuring exact volumes, especially small volumes.
The volume of a liquid is only moderately
affected by pressure, but it is often quite sensitive to changes in
temperature. For this reason, volume measurements made at temperatures
other than ambient (the surrounding) temperature are generally so
indicated when they are reported, as V = 35.89 milliliters (35°C).
The
volume of gases is very much influenced by temperature and pressure.
Thus, any attempt to measure or report the volume of the gas must always
include an indication of the pressure and temperature under which that
volume was measured. Indeed, since gases expand to fill any container
into which they are placed, the term volume has meaning for a gas *only*
when temperature and pressure are indicated.
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