Density (Junior Cert Science): Revision Notes

Density

What is density?

Density is a fundamental property of materials that helps us understand how much matter is packed into a given space. When we look at different materials, even if they have the same size or volume, they can have very different masses. This difference is due to their density.

Think about it this way: if you have two identical boxes, one filled with feathers and one filled with rocks, they would feel very different when you try to lift them. The box with rocks is much heavier because rocks have a higher density than feathers. The rocks have more mass packed into the same volume.

The diagram above shows cubes that are all the same size (they have equal volumes). However, they have very different masses. Lead has a mass of $11.3 \text{ g}$, while polystyrene (a type of plastic foam) has a mass of only $0.02 \text{ g}$. This demonstrates that different materials have different densities.

Understanding density helps us explain many everyday observations. For example, why does iron sink in water but wood floats? Why are some materials chosen for building aeroplanes while others are not? The answer lies in their densities.

The density formula

To calculate the density of any material, we use a simple mathematical formula that relates three important quantities: density, mass, and volume.

The formula is:

$\text{density} = \frac{\text{mass}}{\text{volume}}$

This can be remembered using the triangle method or the abbreviation "DMV":

• D = Density
• M = Mass
• V = Volume

The unit for density is grams per cubic centimetre, written as $\text{g/cm}^3$. This tells us how many grams of material are present in one cubic centimetre of space.

Calculating density

To find the density of any object, you need to follow four clear steps. Let's work through the process systematically.

Step 1: Find the mass Use a balance or scales to measure the mass of the object in grams.

Step 2: Find the volume For regular shaped objects (like cubes or rectangular blocks), calculate the volume using: $\text{volume} = \text{length} \times \text{width} \times \text{height}$

For irregular shaped objects, you can use the water displacement method (described in experiments).

Step 3: Use the density formula Write down the formula and substitute your values: $\text{density} = \frac{\text{mass}}{\text{volume}}$

Step 4: Write the answer with correct units Always include $\text{g/cm}^3$ with your answer.

Density values of different materials

Different materials have very different densities. This table shows the densities of common substances, organized by whether they are lighter or heavier than water.

The density of water is $1 \text{ g/cm}^3$, which makes it a useful reference point. Substances with densities lower than $1 \text{ g/cm}^3$ will float on water, while substances with densities higher than $1 \text{ g/cm}^3$ will sink.

Substances lighter than water

These materials have densities less than $1 \text{ g/cm}^3$:

Substance	Density (g/cm³)
Expanded polystyrene	0.02
Cork	0.3
Paraffin oil	0.8
Ice	0.9
Polythene	0.9

Substances heavier than water

These materials have densities greater than $1 \text{ g/cm}^3$:

Substance	Density (g/cm³)
Aluminum	2.7
Lead	11.2
Mercury	13.6
Gold	19.3
Osmium	22.6

Osmium is the densest naturally occurring element. A small piece of osmium would feel incredibly heavy for its size because it has so much mass packed into a small volume.

Density of gases

Gases also have density, although their densities are much lower than solids and liquids because the particles are much more spread out.

Gas	Density (g/cm³)
Helium	0.0002
Air	0.0013
Carbon dioxide	0.0020

Helium has a lower density than air, which is why helium balloons float upwards. Carbon dioxide has a higher density than air, which is why it sinks and can collect in low-lying areas.

Why is density important in our everyday lives?

Understanding density helps us explain many phenomena we observe in daily life and allows engineers and designers to create useful products.

Flotation

Knowledge of density helps us predict whether objects will float or sink in liquids. This principle is called flotation.

An apple floats on water because it has a lower density than water (approximately $0.8 \text{ g/cm}^3$). The apple slice may initially sink because cut fruit can absorb water, but a whole apple with air pockets inside typically floats.

The density column experiment demonstrates this principle beautifully. Different liquids are layered according to their densities:

• Syrup (highest density) sinks to the bottom
• Water sits in the middle layer
• Oil (lowest density) floats on top

Objects placed in the column settle at different levels:

• The ping-pong ball floats at the very top (lowest density)
• The nail lies at the bottom

This happens because each object sinks until it reaches a liquid layer that has a higher density than itself.

Practical applications of flotation:

Helium balloons float in air because helium gas has a much lower density than air. This principle is used for party balloons, weather balloons, and even airships.

Identifying substances

If you know the density of a substance, you can identify what material it is made from. Different materials have unique densities, like a fingerprint. This is particularly useful for identifying rocks and minerals, or for detecting fake jewellery.

Geologists use density to help identify rock types. For example, if you find a rock and measure its density to be around $2.7 \text{ g/cm}^3$, it might be granite.

Design of lightweight objects

Engineers use materials with low density to make objects easier to carry and more efficient.

Modern aeroplanes are designed using metals with relatively low density, such as aluminum ($2.7 \text{ g/cm}^3$). This makes the aircraft light enough to fly efficiently while still being strong. Engineers carefully choose materials that are both strong and lightweight.

Laptops and mobile phones are also designed using low-density materials where possible. This makes them portable and easy to carry around. The cases are often made from lightweight plastics or aluminum alloys.

Formula 1 racing cars use low-density carbon fiber materials. Keeping the car's mass as low as possible helps it accelerate more efficiently and use less fuel. The materials must also be strong to protect the driver, so engineers select materials with the best strength-to-density ratio.

Why does an iron ship float?

You might wonder why a massive iron ship can float when a small piece of iron sinks in water. Iron has a density of about $8 \text{ g/cm}^3$, which is much higher than water's density of $1 \text{ g/cm}^3$. So why doesn't the ship sink?

The answer lies in the average density of the entire ship. While the iron hull itself is denser than water, the ship contains large air pockets and compartments. These include the deck areas, cabins, and cargo holds.

When you calculate the total mass of the ship (including the iron and the air inside) and divide it by the total volume (including all the hollow spaces), the average density of the whole ship is less than the density of water. This is why the ship floats.

Ships also have ballast tanks which can be filled with water to increase the ship's density and make it sit lower in the water (for stability), or emptied to decrease density. This helps control how the ship floats and maintains balance.

Remember!