Volume and mass are two concepts that are at the core of measuring amounts, both in science and in life at large. In simple terms, volume measures the amount of space occupied by an object or material, while mass measures the amount of matter that makes up that same object or material. Intuitively, most people see the link between these two concepts. They will expect larger objects to have more mass, and smaller objects to have less, and often they will be right. Understanding the two concepts fully is key to knowing why this generalization is not always true.
Volume is an easily observed concept. At an early age, children learn that a glass can only hold a certain amount of milk. If they want more, they either need a second glass, or a bigger glass. There is absolutely no way that they can fit a half gallon (or two liters) of milk into a single glass at once, because a half gallon of milk takes up a half gallon of space, every single time. The persistent child might make a few messes on the way to learning this, but ultimately the concept of “bigger” and “smaller” amounts takes hold.
As the child learns, volume is a fancy word for three-dimensional size. In the case of box-like objects, the formula “length times width times height” serves them well. Other regular shapes like spheres (“four thirds pi times radius cubed”) aren’t too difficult either. Irregular objects pose more of a challenge, until the concept of displacement is introduced. Dunking a solid object in water (or some other liquid) causes the water to move, either rising within the container or overflowing. Either way, the volume of the water moved (displaced) is easily measured, and is equal to the volume of the object being dunked.
Volume applies to solids, liquids and gasses, but measuring them is achieved in different ways. The volume of solids may be measured with rulers (or calipers) and formulas, or by displacement, as discussed. Liquids are measured using containers that are of known size (and possibly graduated with intermediate markings as well). Gasses are trickier, as a gas will expand to fill whatever container it is placed in. Without information about the environment (pressure and temperature) a gas is in when it is measured, volume is not very meaningful for gasses.
Measures of volume are numerous, encompassing just about any container size ever invented. Historically you might find the ancient Greek “batos” (about 39 liters, enough for a bath), the virtually never used American “dram” (about 3.6 milliliters), and the much more popular fifth (1.3 liters) that pleases vodka lovers so. From Sweeden we know that a “jumfru” would make a single swallow, while Egypt’s “qadah” is enough soda for a family to enjoy with dinner*. For the most part though, and particularly in the science community, the world has standardized on the liter as the basic unit of volume. A liter is equivalent to a cube that is exactly ten centimeters on a side. For smaller or larger volumes, metric prefixes are used, making units like milliliters (one thousandth of a liter) or nanoliters (one billionth of a liter) possible. In the other direction, an ocean of information can be conveyed with the unit Megaliters (one million liters).
Mass is a less intuitive concept than volume. Since it measures the amount of matter (and energy, which makes a small contribution, but will be ignored for this discussion) in an object or material, the pre-requisite is an understanding of what matter is. During childhood, it is normal to develop a concept of weight – some objects are heavier than others. Weight is related to mass, but not the same. Weight refers to the force of gravity on an object, and the perception of weight is impacted by things like buoyancy, shape, and other surrounding factors. Mass is an absolute measure of the amount of matter in an object (think of it as the sum of the protons and neutrons that make it up for a good first estimate). It seems obvious that objects with a lot of matter should weigh more than an object with less matter, but the issue gets confused when people see a blimp (which has a great deal of matter in it) floating through the sky, seemingly weightless. Weight also is dependent on the local gravity, so three objects of equal mass located at Earth’s North pole, Earth’s equator (where gravity is slightly less, due to Earth’s bulging), and on the surface of the moon (with less gravity) all have different weights. Separating the idea of weight (downward force) from mass (amount of matter) is an important first step in making sense of mass measurements.
All matter has mass. Even a single electron, tiny as it is, possesses a miniscule, measurable amount of matter. Whatever object is being discussed, so long as the number and type of atoms that makes it up is kept constant, the mass of the object does not change. A glass sculpture (mostly silicon and oxygen atoms) will have the same mass anywhere it is measured, be it Austria, Cuba, or Mars.
Measuring mass is a little trickier than measuring volume. Directly counting the protons and neutrons in an object is still beyond modern technology. Mass is instead measured using a balance – an instrument that compares one object to another object (or objects) of known mass. The simplest balance design has been used for centuries. Also referred to as “scales”, two pans are suspended at equal distances from the central point of a rod. They hang level when the mass on both sides is equal. To one side of the scale is added the unknown object, and weights of known mass are added to the other side. When balance is achieved, the two masses are equal, and the unknown mass has been determined. More modern balances may use calibrated springs or other mechanical devices to achieve the same result, but ultimately the principle is the same – mass is determined by comparison to another known mass. (Standard masses are defined and maintained by governments and scientific institutions for this purpose.)
Mass measurements made using balances rely on weight. (This is another reason that people tend to get the two confused.) This means that buoyant objects can pose a challenge (try measuring a helium balloon on a scale). In such cases, environment plays a big factor. A balance can in fact be used to measure the mass of a helium balloon, if the balloon and balance are sealed inside a vacuum, where the balloon is no longer buoyed up by surrounding air. Other challenges exist for making precision mass measurements. Single molecules or atoms do not have enough mass to show up on a balance. Scientists can use an instrument called a spectrometer to determine such small masses. Even so, the mass is a comparison to known, defined masses. The ultimate mass reference is a single atom of carbon-12, defined to have a mass of exactly 12 atomic mass units. All other modern measurements of mass can be related to this value, providing universal conversion factors.
Units of mass are every bit as plentiful as units of volume. The “carat” is a popular for diamonds and other gems (0.2 grams). The Chinese “chien” and the Japanese “momme” are both roughly 4 grams, the South American “libra” is a little less than half a kilogram, and is roughly equivalent to the “pound” which is a measurement of weight that citizens of the United States frequently confuse for mass.* (Fortunately, so long as they stay on Earth, weight and mass are proportionate.) The internationally (and scientifically) agreed upon unit of mass is the gram, and all of its metric derivatives. As with the liter, they exist in multiples of tens and thousands, so the kilogram is one thousand grams.
Mass and volume are linked by the concept of density. Density is defined as mass divided by volume. Density is an identifying property, useful since it varies greatly between different elements and compounds. Density is a constant for any given material, so long as temperature and pressure remain constant. Materials tend to increase their volume when heated (which lowers density), and an increase in pressure can compress objects to smaller volumes. (Solids and liquids cannot be compressed much, but gasses can be compressed to small fractions of their initial volume.) A decrease in volume results in a higher density.
Density is a concept that most people grasp long before they understand mass. They know that a handful of feathers will always weigh less than a handful of rocks, and that if a truckload of gold bars ever comes along, they’re going to cart it away bar by bar, and not try it by the crate, lest they hurt their backs.
Because density is a derived quantity – a measurement calculated from two other measurements, it doesn’t get its own units. Instead, it is described in terms of the mass and volume units used to determine it – usually grams / milliliters (g/mL) for liquids, grams / cubic centimeters (g/cm3) for solids, and grams / liter (g/L) for gasses. (Cubic centimeters are equal to milliliters, but the preference exists nonetheless.)
*Obscure units and conversion factors found in “Measure for Measure” by Young and Glover; Sequoia Publishing, Inc. of Littleton, Colorado – 2004.