Study Material

# Density

We explain what density is, its formula, how to calculate it, the types that exist and we give several examples. How is density measured

## What is density?

The mass density of a substance is the quotient between the mass of the sample and the volume it occupies, its unit of measurement being kg / m 3 in the International System of Units. The Greek letter ρ (rho) is often used to denote it.

The density of water, which is the universal fluid, is 1000 kg / m 3 or 1 g / cm 3 at 25 ºC, since the density undergoes changes with temperature and pressure. How is density measured

Objects with the same dimensions are often found, and yet some are lighter and others are heavier, this is due to differences in density. The lightest object has a lower density than the heaviest.

Density is an intensive property of matter , which does not depend on the amount of mass of the sample being examined, since it is the mass / volume ratio that remains constant for the same substance. This makes it possible to differentiate one substance from another. How is density measured

The concept of density is especially useful when working with continuous media such as fluids, whether they are gases or liquids.

## Density formula

According to the definition given, the density has a mathematical formula given by: How is density measured Where the density is ρ, m is the mass and V the volume.

## How is density measured?

The density of an object can be calculated if its mass and volume are previously measured. The latter is not always easy, as the sample can be irregular, however there are several methods.

### Geometric method How is density measured

If the sample has a regular geometric shape, there are formulas that allow the volume to be calculated based on its dimensions. As for the mass, this can be obtained with the help of a balance.

### Test tube method: volume displacement

If the object is not regular, its volume can be determined by measuring the volume displaced by completely submerging it in a fluid such as water. How is density measured

To use this method, the substance in the sample must not dissolve in the water and a graduated container of the appropriate size must be available. How is density measured

### Density using Archimedes’ principle

Archimedes’ principle can be used to find the density of a solid sample. The principle states that a body partially or totally submerged in a fluid experiences an upward force called thrust, whose magnitude is equal to the weight of the fluid displaced when placing the body.

To determine the density of an object using Archimedes’ principle, the following steps are followed:

• #### Step 1 How is density measured

Determine the mass m c of the object using a balance.

• #### Step 2

Fill a container with a fluid whose density is known, which is usually distilled water. This value is called m 1 .

• #### Step 3 How is density measured

Completely submerge the solid object in the container with water, taking care that it does not touch the walls. It is observed that the fluid exerts an upward push E on the solid, and this in turn, by Newton’s third law, exerts a reaction of equal magnitude on the water, but in the opposite direction.

When weighing the whole, the value obtained, called m 2 , will be that of the container filled with water plus this reaction.

• #### Step 4 How is density measured

From the equation for density, we can express the volume V of the body, which is equal to the volume of fluid displaced:  The mass of the dislodged fluid m f is simply:

f = m 2 −m 1

Therefore: ## Density types

### Absolute density How is density measured

It is the density as defined above: the ratio of the mass to the volume of the sample. ### Relative density

Also called specific gravity , it is the density of one substance with respect to another that is taken as a reference. For solids and liquids this reference substance is water at 4ºC and 1 atm of pressure and for gases it is dry air. It is calculated by:

Relative density = density of material / density of water

Both the density of the material and that of the water must be measured under identical conditions of pressure and temperature, and expressed in the same units.

The following image shows the relative densities of steel and wood. How is density measured

Since the density of steel is 7800 kg / m 3 and that of water is 1000 kg / m 3 , the relative density of steel, denoted sg, is:

sg = 7800/1000 = 7.8

For its part, the relative density of wood is:

sg = 500/1000 = 0.5

Objects whose relative density is less than 1 float on water, while those whose relative density is greater than 1 sink.

### Apparent density

It is calculated by the quotient between the mass of the sample and its volume, including pores and spaces with air:

Apparent density = Mass / Volume = ( Particle mass + Air mass ) / ( Particle volume + Air volume )

## Examples of density

• The lightest metal of all is lithium, with a density of 530 kg / m 3
• The density of blood is 1060 kg / m 3
• Osmium is the densest metal known, with a density of 22 570 kg / m 3
• The quark plasma has a density of 1 × 10 19 kg / m 3

## Solved exercises

### Exercise 1 How is density measured

Calculate the density of the cork, knowing that a cube made with this material, which measures 1.5 cm on a side, has a mass of 1 g.

• #### Solution

The volume of a cube is:

V = ℓ 3 = (1.5 cm) 3 = 3.375 cm 3

The statement indicates that the mass m of the cube is m = 1 g, therefore, substituting values ​​in the density equation:

ρ = m / V = ​​1g / 3.375 cm 3 = 0.296 g / cm 3

### Exercise 2 How is density measured

What is the mass of a sphere made of osmium with a radius of 15 cm?

• #### Solution

Starting from the density equation: The mass is cleared as:

m = ρ ∙ V

It is necessary to calculate the volume of the sphere, which is given by the formula: Where r is the radius of the sphere. Since the density of osmium is 22570 kg / m 3 , it is convenient to express the 15 cm in meters:

r = 15 cm = 15 × 10 −2 m

V = (4/3) π × (15 × 10 −2 m) 3 = 0.01414 m 3

This value is substituted in the clearance for the mass:

m = ρ ∙ V = 22570 kg / m 3 × 0.01414 m 3 = 319.1 kg

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