Have you ever wondered why ships float in the sea? Or why does ice form at the top surface of water first? Density lies at the centre of the answer to these questions. This article will delve into density, how it is measured and what it is used for.
Density measurement definition
Density, as a concept, is essentially the compactness of a material or an object. In lay terms, it measures how much matter can fit into a given space.
Imagine you have two identical cardboard boxes. You put ten coffee mugs in box A and 20 in box B. Which one do you think is denser? The two boxes are identical, but the amount of stuff in them differs. Even though they both have the same volume, box B has more things than box A. So, box B is denser than box A.
Does that make sense? In general, the more matter or substance is crammed into a given space, the denser it becomes.
In science, the amount of matter in an object is defined as the object's mass, measured in kg. The amount of space is defined as volume, which is measured in m3. Therefore, the scientific definition of density is the mass per unit volume, and its unit is kg/m3.
$$\text{Density (kg/m\(^3\))}=\dfrac{\text{Mass (kg)}}{\text{Volume (m\(^3\))}} \text{ or }\rho=\dfrac{m}{V}$$
$$\rho=\text{Density}$$
$$m=\text{Mass}$$
$$V=\text{Volume}$$
Water (H2O) has a density of roughly 1000 kg/m3, while air has a density of approximately 1.2 kg/m3.
- Liquids tend to be denser than gases in general.
- And solids are often even denser than liquids.
This is due to the closer arrangement of molecules in solids and liquids compared to gases.
Let's go through a simple example of calculating density.
A cube weighs 5 kg (i.e., it has a mass of 5 kg). Each of its sides is 10 cm in length. What is the cube's density?
We know the cube's mass but need to calculate its volume. The formula for the volume of a cube is height x width x length.
The length of our cube is 10 cm or 0.1 m, and we know that the height and width of a cube are the same. So, the volume of the cube is 0.1 x 0.1 x 0.1 = 0.001 m3.
Density is mass over volume. Hence, the cube's density is:
$$\text{Density of the cube}=\dfrac{5}{0.001}=5000\text{ kg/m\(^3\)}$$
Density is an intensive property, meaning it doesn't depend on the amount of material. The density of one brick could be the same as the density of a hundred bricks.
Colour, temperature and density are examples of intensive properties.
An intensive property is a material's property determined only by the type of matter in a sample and not by its quantity.
Methods of measuring density
To measure the density of an object, we must first calculate its mass and volume. Measuring the mass is straightforward. All we need is to place the object on a balanced scale. The scale would then give us the mass. However, measuring the volume is not so straightforward - objects either have a regular or irregular shape, which determines how their volume can be calculated.
When measuring the volume of an object, two factors need to be recorded: pressure and temperature.
Pressure is inversely proportional to volume, meaning the volume increases as pressure decreases. This is particularly significant in gases as the gas molecules are not bound to each other and freely moving around.
Temperature, on the other hand, is often directly proportional to volume. As materials get warmer, the molecules have more energy, so they are excited and moving apart. This results in the materials expanding as the temperature increases.
Since the mass of an object is constant and does not change, the temperature is inversely proportional to density, while pressure is directly proportional.
Ice is an exception to the concept mentioned above. Below 4°C, water expands instead of shrinking due to the unique arrangement of water (H2O) molecules and hydrogen (H) bonds between them. As a result, ice has a smaller volume than liquid water per unit mass. This translates into solid ice being less dense than liquid water. Now you know why icebergs float in oceans!
Measuring the volume of regular objects
A regular object is defined as an object whose volume can be measured by relatively simple calculations.
Such as a cube. This is a regular shape because we can calculate its volume by multiplying its height by width and length.
Another regular object is a sphere. We can measure the sphere's diameter and radius by simple measurements. Then we can use the equation below to calculate the volume of our spherical object.
$$V=\dfrac{4}{3}\pi r^3$$
Where \(r\) is the radius and \(V\) is the volume of the sphere.
Measuring the volume of irregular objects
Measuring the volume of irregular objects is trickier. They often have asymmetrical and crooked shapes that make calculating their density nearly impossible. But luckily, there is a more clever method that allows us to measure the volume of any object. This method is based on Archimedes' discovery, also called the Archimedes' principle.
Archimedes' principle states that when an object is at rest in a fluid, the object experiences a buoyant force equal to the weight of the fluid that the thing has displaced. If the object is entirely immersed in the liquid, then the volume of fluid displaced equals the object's volume.
So by measuring the change in the fluid's volume, we can calculate the volume of the object submerged in it.
The instrument for measuring density
A helpful instrument used for measuring the volume of irregular objects is a Eureka can that can be filled with water and an empty measuring cylinder. Eureka cans have an outlet on the side that allows the excess water to flow out. This water can then be collected by the measuring cylinder next to it. So, in theory, as long as the eureka can is filled up to the outlet, the amount of water poured out into the measuring cylinder when a solid object is added to the can is precisely equal to the object's volume.
After obtaining the volume of our object, we then have to divide its mass by this volume to find its density.
Eureka cans are named after Archimedes, the ancient Greek scientist who initially discovered fluids are displaced by the same volume as the object submerged in them.
Measuring the density of liquids is a lot easier. We must place an empty measuring cylinder on a balanced scale and zero the balance to reset it. Now, if we add some liquid to the cylinder, the scale would give us its mass, and the measuring cylinder would provide us with its volume. Then we have to divide the liquid's mass by its volume to find the density.
Measuring the volume of gases is slightly trickier. But using a laboratory tool called a eudiometer makes it straightforward. A eudiometer can measure the volume of a gas mixture produced or released in physical or chemical reactions. It is made of an upside-down graduated cylinder filled with water. A small tube transfers the generated gas into the cylinder, where the gas becomes trapped at the top by water. The reading on the cylinder at the water level gives the volume of the gas at room temperature and pressure.
Units of density measurement
Density is mass over volume. Hence, density's unit would be the unit of mass over the unit of volume. There is a wide variety of measuring units used for volume and mass. For example, the mass of an object can be measured in grams, kilograms, pounds, or stones. Regarding volume, the following S.I. units can be used: cubic metres (m3), cubic centimetres (cm3), cubic millimetres (mm3) and litres (l) to describe the space an object is occupying.
S.I. units are the international system of measuring units used universally to have a standardised method for scientific research.
S.I. units are like different languages for describing the same words, and they can be converted into one another.
A stone of mass 40 kg with volume 8 cm3 calculates its density in g/l.
$$1 \text{ kg} = 1000\text{ g}$$
$$1 \text{ cm}^3 = 0.001\text{ l}$$
$$\text{Density}=\dfrac{40\text{ kg}}{8\text{ cm}^3}=\dfrac{40\times 1000 \text{ g}}{8\times 0.001\text{ l}}=\dfrac{5\times 10^6 \text{ g}}{\text{l}}=5\times 10^6\text{ g/l}$$
Purpose of density measurement
In simple words, the density of an object determines whether it floats or sinks. The purpose of density measurements can be used to design ships, submarines, and aeroplanes.
It is also responsible for currents in the ocean, atmosphere and the earth's mantle.
We discussed the Archimedes principle earlier, and that a fluid exerts a buoyant force on an object inside it that is equal to the weight of the fluid that has been displaced. If this buoyant force exceeds the object's weight, it will float. But if the object's weight is greater than the buoyant force, the object is going to sink.
If the density of a material is greater than that of a fluid, then the buoyant force will not be enough for the material to float, and hence it will sink.
If Dobject > Dfluid, then the object will sink
If Dobject < Dfluid, then the object will float
Measuring Density - Key takeaways
- Density, as a concept, is essentially the compactness of a material or an object.
- The scientific definition of density is the mass per unit volume of an object, and its unit is kg/m3. $$\text{Density (kg/m\(^3\))}=\dfrac{\text{Mass (kg)}}{\text{Volume (m\(^3\))}} \text{ or }\rho =\dfrac{m}{V}$$
- Density is an intensive property, meaning it doesn't depend on the amount of material.
- A Eureka can is used to measure the volume of objects with irregular shapes.
- The density of an object determines whether it floats or sinks:
- If Dobject > Dfluid, then the object will sink
- If Dobject < Dfluid, then the object will float
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