Measuring Volume

Volume is a property of matter that describes the amount of three-dimensional space that an object occupies. Volume is often measured in cubic units, such as cubic centimeters (cm3), cubic inches (in3), cubic meters (m3), or cubic miles (mi3). A cubic centimeter is the three-dimensional space occupied by a cube that is 1 cm × 1 cm × 1 cm.

Other common units of volume include fluid ounces (fl oz), tablespoons (tbsp), quarts (qt), gallons (gal), barrels (bbl), liters (L), and milliliters (mL). 1 milliliter (mL) = 1 cubic centimeter (cm3). So an object that has a volume of 24 mL would occupy the same amount of three-dimensional space as twenty-four cubes each measuring 1 cm × 1 cm × 1 cm.

One way to measure the volume of an object, especially an irregularly shaped object, is by displacement. First, measure the volume of water in a graduated cylinder. Then, add your object to the graduated cylinder, making sure that it is completely submerged in the water. And finally, measure the new volume in the graduated cylinder. The increase in the volume (the amount of water that the object has “displaced”) is equal to the volume of the object itself. This is an indirect measurement since you are not measuring the volume of the object directly.

Reading a Meniscus
Volume on a molecular scale

Volume is a seemingly simple concept when it comes to objects on a macroscopic scale (large enough to be measured and observed by the naked eye), but things get murkier when you consider objects on a molecular scale. On a molecular scale, even a solid contains a lot of empty space. The water molecules in ice occupy more space than their physical volume requires because they are moving. If the water molecules in ice were not moving and you could pack them as close together as possible, an ice cube would occupy much less space.

Interpreting the volume of a gas is even more difficult. A gas will expand to occupy whatever volume is available. If you place a gas in a 20-liter container, its volume will be 20 liters. If you take that same gas and place it in a 200-liter container, its volume will be 200 liters. And if you compress the gas (squeeze it down) and place it in a 2-liter container, its volume will be 2 liters. The volume of a gas depends on its temperature and how much pressure is on it. Increasing the temperature of a gas increases its volume because the molecules in the gas are moving faster and will take up more space. Increasing the pressure on a gas decreases its volume because the molecules are being pressed closer together.

There are a series of gas laws that describe the relationship between the temperature, pressure, and volume of a gas. These laws have been combined into the ideal gas law: PV = nRT, where P is the pressure, V is the volume, n is Avogadro’s number, R is the gas constant (8.314472 J·K-1·mol-1), and T is the temperature in kelvins (K). An “ideal” gas is a gas in which its molecules have zero attraction to each other. Because all molecules have some attraction to each other, there are no ideal gases in the real world. But when molecules (such as water molecules) are far apart in a gas state, the force of attraction between them is close to zero and the gas will behave almost like an ideal gas (the force of attraction between molecules gets weaker as the molecules get farther apart).

The Compressibility and Expansion of Solids and Liquids

On a macroscopic scale, volume is simply a property of matter that describes the amount of three-dimensional space that an object occupies. On a molecular scale, volume is a little more complicated. It is not only the space physically occupied by a molecule, but also the space occupied by the molecule’s translational motion. Therefore, the volume of an object can and will change (if only very slightly) with changes in the temperature and pressure.