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Measuring Density

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, as…

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Jetzt kostenlos anmeldenHave 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**, 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 **m**^{3}. Therefore, the scientific definition of **density** is the** mass per unit volume, **and its unit is **kg/m**^{3}.

$$\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** (H_{2}O) has a **density** of roughly **1000 kg/m**^{3}, while **air** has a **density** of approximately **1.2 kg/m**^{3}.

**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 m ^{3}**.

**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.

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 (H_{2}O) 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!

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** 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

So by **measuring the change** in the fluid's volume, we can **calculate the volume** of the object submerged in it.

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**.

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 (m ^{3}), cubic centimetres (cm^{3}), cubic millimetres (mm^{3}) 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 cm ^{3} **calculates its

$$1 \text{ kg} = 1000\text{ g}$$

$$1 \text{ cm}^3 = 0.001\text{ l}$$

$$\text{Density}=\dfrac{40\text{ kg}}{8\text{ cm}^3}=\dfrac{40\times 1000 \text{ g}}{8\times 0.001\text{ l}}=\dfrac{5\times 10^6 \text{ g}}{\text{l}}=5\times 10^6\text{ g/l}$$

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

**D**_{object }> D_{fluid}, then the object will**sink**If

**D**_{object}< D_{fluid}, then the object will**float**

- 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/m
^{3}. $$\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 D
_{object }> D_{fluid}, then the object will sink - If D
_{object}< D_{fluid}, then the object will float

- If D

**A stone of mass 40 kg with volume 8 cm ^{3} calculate its density in g/l. **

1 kg = 1000 g

1 cm^{3} = 0.001 l

**Density** = 40 kg / 8cm^{3} = (40 x 1000 g) / (8 x 0.001 l) = **5x10 ^{6} g/l**

A balanced scale, a Eureka can, and a measuring cylinder

**pressure** and **temperature**

Flashcards in Measuring Density13

Start learningWhich is denser?

2 m^{3 }of feathers

What is the standard formula of density?

kg/m^{3}

What two factors need to be recorded while measuring the volume of an object?

Pressure

Archimedes' principle states that when an object is at rest in a fluid, the object experiences a buoyant force double the weight of the fluid that the object has displaced.

False

According to the Archimedes' principle, the weight of water displaced equals the weight of the object immersed in the fluid.

False

All materials expand as temperature increases.

False

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