Heat

This section explores how heat energy causes substances—solids, liquids, and gases—to expand. You will examine the concepts of linear, area, and volume expansion, and how these relate to real-life applications such as bridges, power lines, thermometers, and thermostats. The section provides opportunities to calculate expansion in different materials and to compare the expansivity of various metals. Through experiments and activities, you will gain hands-on experience with devices like bimetallic strips and ball-and-ring apparatuses, deepening your understanding of how thermal expansion affects engineering design and safety.

Prior knowledge from Year One on particle theory and thermometers will be linked to this topic.

KEY IDEAS

· Anomalous Expansion of Water: behaves uniquely by expanding as it cools from 4°C to 0°C, which is essential for aquatic life survival.

· Applications of Thermal Expansion: Thermal expansion affects everyday objects and structures, such as bridges, railway tracks, power lines, thermometers, and thermostats.

· Coefficient of Expansion: Materials expand at different rates; linear, area, and volume expansivities quantify these changes for solids, liquids, and gases.

· Effect on States of Matter: Solids, liquids, and gases expand differently when heated; gases expand the most, followed by liquids, then solids.

· Real-Life Design Considerations: Expansion joints in bridges, sagging of power lines, and gaps in railway tracks are deliberate engineering designs to prevent damage.

Have you ever noticed the behaviour of these everyday objects when they get hot?

Figure 2.1: An electric iron Figure 2.2: Electric Kettle When you switch on an iron to heat it up, you might hear it “click” and see it turn off by itself once it gets hot enough. It then switches on and off repeatedly while you use it. This on-and-off behaviour is closely connected to how the iron’s metal parts behave when heated.

Similarly, have you ever watched an electric kettle boil water? You switch it on, and after a few minutes, it suddenly switches off by itself once the water reaches its boiling point. It seems almost like the kettle “knows” when to stop heating.

But how do both the iron and the kettle know when to stop heating? The answer lies in a process called thermal expansion.

Thermal Expansion

What is thermal expansion?

Thermal expansion is the increase in size of a material when its temperature rises.

Think of it like this: everything is made of tiny, tiny pieces called atoms or molecules. When you heat something, these tiny pieces get more excited and start wiggling and jiggling around faster. As they jiggle more, they push each other a little further apart, making the whole material expand.

Figure 2.3: Thermal expansion of solids This expansion can happen in different ways:

Length: A long, thin object like a metal rod will get slightly longer.

Area: A flat object like a metal sheet will get slightly bigger in both its length and width, increasing its surface area.

Volume: A 3D object like a block of metal, or even liquids and gases, will take up more space.

In solids, these tiny particles are usually packed tightly, but they still vibrate.

When heated, the amplitude of their vibrations becomes larger, pushing them further apart and increasing the overall size of the material. In liquids and gases, particles can move around more freely, so they generally expand even more than solids.

What is happening inside the iron and the kettle?

Inside the iron’s flat metal base and the electric kettle’s metal base and thermostat, the metal parts heat up as electricity passes through. The tiny atoms inside these metals vibrate faster and push each other slightly apart, causing the metal to expand. This is known as thermal expansion.

In the iron, this expansion is detected by a thermostat that switches the heating element off once the metal reaches a set temperature. When the metal cools and contracts, the thermostat switches it back on, causing the iron to click on and off.

In the electric kettle, a special part called a bimetallic strip (usually made from iron combined with another metal like copper) is used. Because the two metals expand at different rates when heated, the bimetallic strip bends as the kettle heats. When enough steam is produced from boiling water, the strip bends enough to trigger a switch that turns off the kettle automatically. As it cools, the strip straightens and resets for the next use.

Applications of Expansion

Where Do We See Thermal Expansion in Real Life?

Thermal expansion is not just a scientific concept; it happens all around us!

1. Bridges and Railway Tracks: Have you ever noticed gaps in bridges or railway tracks? These are called expansion joints. On hot days, materials like steel expand. If there were not gaps, the tracks or bridge could buckle and get damaged!

Figure 2.4: Railway track

2. Sagging Power Lines: On a hot day, you might see electrical power lines hanging lower between poles. This is because the wires expand with the heat.

This sagging is actually a good thing! It prevents the cables from becoming too tight and snapping when they contract in cold weather.

Figure 2.5: Sagging Power lines

3. Stuck Jar Lids: If you have trouble opening a jar with a metal lid, try running it under hot water. The metal lid heats up and expands slightly, making it easier to twist off!

4. Thermometers: The mercury or alcohol inside a thermometer expands when it gets warmer, rising up the tube to show you the temperature.

5. Engines and Machines: The metal parts in engines and machines get very hot when they’re working. Engineers have to design these parts carefully, leaving tiny gaps (called clearances) so that they can expand without getting stuck or wearing out too quickly.

6. Hot Water Heaters: A hot water heater has a special expansion tank. This tank gives the water, which expands as it gets hot, a place to go, preventing damage to the heater.

7. Thermal Fatigue: Imagine something that gets hot and cold over and over again, like parts in an airplane engine. This constant expanding and contracting can eventually make the material weak and cause it to break.

This is called thermal fatigue Bimetallic Strips As mentioned earlier, a bimetallic strip is a special type of material made by bonding together two different metals, such as brass and steel. These metals are chosen because they expand at different rates when heated. When the strip is heated, one metal expands more than the other, causing the strip to bend. This bending occurs because the two metals try to lengthen by different amounts, but are stuck together, forcing the strip to curve. This unique behaviour makes bimetallic strips very useful in devices like thermostats and electric kettles, where the bending action can be used to turn switches on or off based on temperature changes.

Figure 2.6 :Bimetallic strip showing two sides made up of different metals Here is how it works

1. Both metals start at the same length.

2. When heated, one metal expands more than the other because it has a higher “coefficient of linear expansion” (meaning it expands more for the same temperature change).

3. Since they are stuck together, the strip has to bend, with the metal that expanded more on the outside of the curve.

4. When it cools down, the bending reverses.

Figure 2.7: Bimetallic strip when heated and cooled

Figure 2.8: Bimetallic strip being heated Cool Applications of Bimetallic Strips

1. Thermostats: Help regulate temperature by turning heating or cooling devices on and off. They are found in household appliances like irons (to maintain soleplate temperature), ovens, refrigerators, air conditioners, and electric heaters.

2. Fire Alarms: Early fire alarms used bimetallic strips as a simple temperature sensor. When a fire caused the surrounding air to heat up, the strip would bend. This bending would complete an electrical circuit, triggering an alarm bell to ring.

3. Automotive Parts: Bimetallic strips are also used in automotive parts, such as the thermal switches that control engine fans. The strip bends when the engine gets hot, completing a circuit that turns on the cooling fan. Once the engine cools down, the strip returns to its original position, turning off the fan.

4. Circuit Breakers: Bimetallic strips can act as thermal circuit breakers. When excessive current flows through the strip, it heats up and bends, breaking the circuit and preventing damage from overheating. This protects electrical circuits from overloads and short circuits in various applications.

5. Thermometers: Some thermometers use spiral bimetallic strips that uncoil or coil up with temperature changes, moving a pointer to show the reading.

Figure 2.9: Bimetallic thermometer How a bimetallic strip thermometer works · A bimetallic strip, made of two different metals, is coiled into a helix. One metal has a higher coefficient of thermal expansion than the other.

· When the temperature changes, the two metals in the strip expand or contract at different rates.

· This unequal expansion causes the coiled strip to either tighten or unwind.

· One end of the coil is fixed, while the other end is attached to a pointer.

· As the coil winds or unwinds, it moves the pointer along a calibrated scale, which indicates the temperature.

Measuring Expansion: Linear, Area, and Volume

Scientists and engineers have ways to measure exactly how much things expand.

Linear Expansion

This is about how much the length of an object change. It is usually looked at for long, thin things like rods or wires.

Linear expansion refers to the change in length of an object due to temperature change.

A term called linear expansivity or coefficient of linear expansion is used to describe how much a material expands in length for every degree its temperature changes.

Figure 2.10: Linear expansion, showing how the original length (L₁) of a surface increases by ΔL when it is heated and expands.

Linear Expansivity (α): is the fractional increase in length per unit temperature change.

α = ∆l/l₁ × ∆ θ Where, ∆ l = change in length l₁ = initial length ∆ θ = temperature difference You can also find the new length (l₂) after heating:

∆ l = l₂ − l₁ α = l₂ − l₁_ l₁ × ∆ θ l₂ − l₁ = α l₁ ∆ θ l₂ − l₁ = l₁ + α l₁ ∆ θ l₂ = l₁(1+ α ∆ θ) Area Expansion This applies to flat, two-dimensional objects like metal sheets. When heated, both the length and width expand, making the overall surface area bigger.

Area expansion refers to the change in area of an object due to temperature change.

A2

Figure 2.11: Area expansion (also called superficial expansion), showing how the original area (A₁) of a surface increases by ΔA when it is heated and expands. The blue square is the original area, and the dashed outline shows the expanded area.

Area (Superficial) Expansivity (β) tells us the fractional increase in surface area per unit temperature change. The formula for area expansivity is β = ∆A/A₁ × ∆ θ Where, ∆ A = change in area A₁ = initial length ∆ θ = temperature difference The new area (A₂) can be found ∆ A = A₂ − A₁ β = A₂ − A₁_ A₁ × ∆ θ A₂ − A₁ = β A₁ ∆ θ A₂ = A₁ + β A₁ ∆ θ A₂ = A₁(1 + β ∆ θ) It’s interesting to note that for most materials, the area expansivity is approximately twice the linear expansivity (β = 2α).

Proof Let θ represents ∆ θ A₂ = A₁(1+ βθ) …… (1) Original area of sheet, A₁= l ₁× b₁ Where l₁ = original length, b₁= original breadth Final area after rise in temperature, A₂ = l₂ × b₂ But from linear expansivity, l₂ = l₁(1+ αθ) , b₂= b₁(1 + αθ) A₂ = l₂ × b₂ = l₁(1+ αθ) × b₁(1+ αθ) A₂ = l₁ b₁ (1+ αθ)²A₂ = l₁ b₁[1 + 2αθ + (αθ)²] α ²≈ 0 (since α is small) A₂ = l₁ b₁[1 + 2αθ]…….(2) Comparing (1) and (2) β = 2α Volume Expansion This is about how much the volume (the amount of space an object takes up) changes. This applies to solids, liquids, and gases.

Volume expansion refers to the change in volume of an object due to temperature change.

Figure 2.12: Volumetric expansion, showing how the volume of a substance (initial volume V₁) increases by ΔV when its temperature changes. The larger (dotted outline) cube shows the expanded volume after heating Volume (Cubical) Expansivity (γ): describes the fractional increase in volume per unit temperature change. The formula for volume expansivity is γ = ∆V/V₁ × ∆ θ Where ∆ V = change in volume V₁ = initial volume ∆ θ = temperature difference The new volume (V₂) is calculated as ∆ V = V₂ − V₁ γ = V₂ − V₁_ V₁ × ∆ θ V₂ − V₁ = γ V₁ ∆ θ V₂ = V₁ + γ V₁ ∆ θ V₂ = V₁(1+ γ ∆ θ) For most solids, the volume expansivity is approximately three times the linear expansivity ( γ = 3α ) Proof Let θ represents ∆ θ V₂ = V₁(1+ γθ) …… (1) Original volume of sheet, V₁ = l₁ × b₁ × h₁ Where l₁ = original length, b₁= original breadth, h₁ = original height Final volume after rise in temperature, V₂ = l₂ × b₂ × h₂ But from linear expansivity, l₂ = l₁(1+ αθ) , b₂ = b₁(1+ αθ), h₂ = h₁(1+ αθ), V₂ = l₂ × b₂ × h₂ = l₁(1+ αθ) × b₁(1+ αθ) × h₁(1+ αθ) V₂ = l₁ b₁ h₁ (1+ αθ)³V₂ = l₁ b₁ h₁(1+ 3αθ + 3 α²θ²+ α³θ³But α ²≈ α ³≈ 0 (since α is small) V₂ = l₁ b₁ h₁(1+ 3αθ)…… .. (2) Comparing (1) and (2) γ = 3α Different Metals, Different Expansion Rates Not all metals expand the same amount when heated! The coefficient of linear expansion (α) is different for different metals. This difference is due to their unique atomic structures and how their atoms are bonded together.

Here is a general idea of how common metals expand (from less expansion to more expansion)

Table 2.1: Some metals and their coefficient of linear expansion Metal Coefficient of Linear Expansion α 10⁻⁶K⁻¹) Steel 11–13 Cast Iron ~10 Brass 19–21 Copper 16.5–17.5 Aluminium 22–24 Zinc 30 Lead 29–31 Metals with Low Expansion These metals are ideal for applications where maintaining a stable size is critical, even with temperature fluctuations.

Steel and Cast Iron (10 – 13 × 10⁻⁶K⁻¹) These are strong and do not expand much, making them perfect for building things that need to stay a specific size. In construction, they are used in the framework of tall buildings, bridges, and railway tracks. The low expansion rate helps these massive structures remain stable and prevents them from buckling or cracking. In cooking, cast iron pots and pans maintain their shape and size even when heated to high temperatures, ensuring they cook food evenly and last for many years.

Metals with Medium Expansion

Engineers must account for the expansion of these metals when designing products, often by including small gaps or using flexible joints.

Brass and Copper (α≈17 − 21 × 10⁻⁶K⁻¹) These metals expand more than steel but are excellent conductors of heat and electricity. In bimetallic strips, because brass expands more than steel, the two metals are bonded together to create bimetallic strips. These are used in thermostats to automatically turn heating and cooling systems on and off by bending with temperature changes. In plumbing, copper pipes are widely used for carrying hot water. They expand when the water is hot, which is why plumbers often use flexible connectors or leave small gaps to allow for this movement without causing leaks.

Metals with High Expansion

These metals are often chosen for applications where a large expansion is a desired or manageable effect.

1. Aluminium and Zinc (α≈22 − 30 × 10⁻⁶K⁻¹) These metals have relatively high expansion rates. In Window Frames, Aluminium is a popular choice for window frames. Its high expansion rate means that when it gets hot, it expands more than the glass. Engineers use flexible seals and clever design to prevent the glass from breaking. In Galvanisation, Zinc is used to coat steel (a process called galvanisation) to prevent rust. The difference in expansion rates between the zinc coating and the steel is a factor that engineers must consider to ensure the coating remains intact.

2. Lead (α≈29 − 31 × 10⁻⁶K⁻¹) Lead has one of the highest coefficients of thermal expansion among common metals. In Sealing, historically, lead was used in plumbing joints because it is soft and flexible. Its high expansion rate helped create a tight seal when heated, but it has largely been replaced due to health concerns.

Anomalous Expansion of Water

Have you ever placed a full bottle of water in the freezer and found it burst open? If not – have a go! This is a common occurrence many people experience but might not fully understand. The reason behind this surprising event is water’s unique and unusual behaviour as it cools down — something known as the anomalous expansion of water.

Unlike most substances that shrink continuously as they get colder, water behaves differently below 4°C. When cooled from room temperature down to 4°C, water shrinks as expected. However, below this temperature, instead of getting denser, it actually begins to expand. This expansion continues as it freezes into ice at 0°C, which is why ice floats on liquid water rather than sinking.

So, when you put a fully filled bottle of water in the freezer, the water expands as it freezes and needs more volume than the bottle can contain. Since the bottle is sealed and rigid, the expanding ice pushes against its walls until it bursts. This simple everyday example highlights a vital and fascinating property of water that is quite different from most other materials.

Figure 2.13: This image represents how the volume of 1 kg of water changes with temperature near 0–10 °C, showing that water reaches its minimum volume (maximum density) at around 4 °C.

The scientific reason for this anomaly (abnormal behaviour) lies in the molecular structure of water. Water molecules are polar and tend to form hydrogen bonds with each other. At temperatures above 4°C, water molecules move more freely and can pack closer together. But below 4°C, those hydrogen bonds arrange molecules into a more open, hexagonal lattice structure. This lattice requires more space, making the water less dense as it cools further and eventually freezes into solid ice.

This unusual property of water has profound implications for life and nature. For instance:

1. Because ice is less dense and floats, lakes, rivers, and ponds freeze from the surface downward, creating an insulating layer of ice on top of the water.

This insulation prevents the water below from freezing solid, enabling fish and other aquatic organisms to survive harsh winter conditions.

2. If water behaved like most other substances and contracted upon freezing, ice would sink, causing entire bodies of water to freeze from the bottom up. This would be devastating for aquatic ecosystems and disrupt countless natural processes.

Figure 2.14: Large iceberg floating in the ocean

Activity 2.1 Exploring Thermal Expansion in Solids, Liquids, and Gases Objective: Observe through videos how heat causes expansion and contraction in solids, liquids, and gases, identify real-life examples of thermal expansion, and understand the different ways each state of matter responds when heated.

What you need

1. A device with internet access (computer, tablet, or smartphone)

2. Access to these videos on YouTube

a. Thermal Expansion and Contraction of Solids, Liquids and Gases

— observe the full video

b. Thermal Expansion | Some Applications Of Thermal Expansion In Everyday Life | Evergreen Publications — observe the first 1 minute

c. Additional video: Thermal Expansion Explained — Observe

3. Notebook or digital notes app for recording your observations and reflections

4. Pen or keyboard What to do

1. Watch or listen to the first video completely. Observe how solids, liquids, and gases expand and contract when heated.

2. Take notes on examples and explanations given, including key ideas about particle movement and thermal energy causing expansion.

3. Watch or listen to the first minute of the second video. Note everyday examples given for thermal expansion.

4. Watch or listen to the third video completely.

5. Fill in the table below with information from the videos and your own understanding State of Matter How it Expands When Heated Examples Tick which of them expand the most when heated Solid Liquid Gas

6. Think, reflect, and discuss in pairs using the following questions

a. Why do we provide expansion gaps in railways and bridges?

b. How can knowledge of thermal expansion be useful in daily life?

Activity 2.2 Research & Create a Report or Poster about Bimetallic Strips Objective: To understand what a bimetallic strip is, how it works, and where it’s used, then present your findings clearly with diagrams.

What you need

1. Device with internet access (computer, tablet, or smartphone)

2. Access to reliable online resources (articles, videos, websites) for research

3. Notebook or digital document for notetaking

4. Paper, pens, markers, or digital tools for creating your report or poster

5. Drawing materials or software to create diagrams (hand-drawn or digital) What to do

1. Open Your Research Tool

Use your internet-connected device to begin your research. You can use search engines (like Google, Bing, DuckDuckGo) or educational websites.

2. Follow the Headings

Conduct your research focusing on answering the questions under these specific headings. As you find information, write down key points, definitions, and facts in your notebook under each heading. Try to use your own words rather than copying word-for-word from the search results!

a. What is a bimetallic strip?

i. Search terms: “What is a bimetallic strip?”, “bimetallic strip definition”.

ii. Look for information explaining what it’s made of and its basic structure.

b. How does it work?

i. Search terms: “How does a bimetallic strip work?”, “bimetallic strip principle”, “thermal expansion bimetallic strip”.

ii. Look for explanations about how the two different metals react to heat and cold, and why it causes the strip to bend. Try to understand the concept of different rates of expansion.

c. Where is it used?

i. Search terms: “Applications of bimetallic strip”, “devices using bimetallic strip”, “bimetallic strip in thermostats”. Find examples of everyday devices or industrial applications that use bimetallic strips.

ii. Think about anything that controls temperature

3. Gather Diagrams

As you research, look for clear diagrams of a bimetallic strip. Save images if you’re working digitally or be prepared to sketch them accurately if creating a physical report.

4. Decide if you want to create a concise Brief Report or an Informative Poster.

a. If creating a Brief Report

i. On a fresh page or in a new digital document, title it: “Bimetallic Strip: An In-Depth Look.”

ii. Organise your findings under clear headings: “What is a bimetallic strip?”, “How does it work?”, and “Where is it used?”.

iii. Write your answers in your own words, making them clear and easy to understand.

iv. Draw or insert at least two diagrams: one showing a bimetallic strip (labelled with the two metals) and another showing how it bends when heated. Label your diagrams!

b. If creating an Informative Poster

i. Grab your large paper/poster board or open your digital design tool.

ii. Create an engaging title, like “Bimetallic Strip: Unveiling Its Secrets!”

iii. Arrange your information clearly using the same headings: “What is a bimetallic strip?”, “How does it work?”, and “Where is it used?”. Use bullet points, short paragraphs, or concise phrases.

iv. Draw at least two large, clear, and well-labelled diagrams. Show what a bimetallic strip looks like, and crucially, how it bends when heated (and perhaps when cooled). Use colours to make your diagrams stand out!

v. Make your poster visually appealing with neat handwriting/fonts and a good layout.

Activity 2.3 Experiment with a Bimetallic Strip or Ball-and-Ring Apparatus Objective: Perform an experiment to observe how heating affects a bimetallic strip or a ball-and-ring apparatus.

What you need

1. Option 1: Bimetallic Strip Experiment

a. Bimetallic strip

b. Clamp or stand to hold the strip

c. Heat source (e.g., spirit burner, candle, or hot water)

d. Thermometer – infrared/forehead (optional)

e. Ruler (optional to measure bending)

2. Option 2: Ball-and-Ring Apparatus

a. Ball and ring set (metal ball that just fits through a metal ring at room temperature)

b. Heat source to heat the ball

c. Icy water to cool the ring

d. Tongs or protective gloves for handling hot metal

3. Notebook or paper to record observations

4. (Optional) Access to a video demonstrating these experiments if you do not have the materials Caution This experiment should be done in a small group of 3-4 people and under the guidance of a teacher. Be careful when handling heat sources and hot materials to avoid burns and accidents.

What to do Bimetallic Strip Experiment

1. Place the bimetallic strip securely in a clamp or hold one end firmly so it can bend freely. Observe if the strip is straight at room temperature.

2. Heat one end of the strip gently with the flame or hot water, taking care not to burn yourself.

3. Watch carefully what happens to the free end of the strip as it heats. Note which direction it bends (up or down).

4. If possible (with the aid of an infrared/forehead thermometer), note the temperature after each increase or at specific time intervals and observe changes.

5. After heating, remove the heat source and let the strip cool down. Observe if and how the strip returns to its original shape.

6. Record all observations clearly, describing how the strip bends during heating and cooling.

Ball-and-Ring Apparatus

1. Check that at room temperature, the metal ball passes through the ring.

2. Heat the metal ball using a flame or hot water until it’s warm (carefully handle it with tongs or gloves).

3. Try to pass the heated ball through the ring.

4. Observe if the ball fits or not and record your observations.

5. Let the ball cool down and check again if it fits through the ring.

6. Once fully cooled, repeat the experiment but this time leave the ball at room temperature and submerge the ring into icy water. Leave it for 2-3 minutes to cool and then lift it out and see if the ball still fits through it.

7. Describe what happened and why in your notes.

If You Do Not Have the Materials

If you do not have these items or cannot do the experiment, you can observe demonstration videos online. Search for terms like “bimetallic strip heating experiment” or “ball and ring thermal expansion” to find clear videos. Observe carefully and write down what is happening in the videos.

Activity 2.4 Material Expansivity Challenge

Objective: To understand how different metals expand at different rates and to discuss why this property is crucial when choosing materials for construction and engineering projects.

What you need

1. Your notebook or a digital document for recording your answers.

2. Pen or pencil.

3. Access to the internet (optional, if you want to verify or find more examples) What to do

1. Examine the Table: Look carefully at the table below, which shows the coefficient of linear expansion (α) for several common metals. This coefficient tells you the factor by which a material expands per degree Celsius for each unit of its original length.

Metal Coefficient of Linear Expansion (α) (per °C) Steel 1.2×10⁻⁵ Aluminium 2.3×10⁻⁵ Copper 1.7×10⁻⁵ Brass 1.9×10⁻⁵ Iron 1.2×10⁻⁵2. Rank the Metals: In your notebook, list the metals from the table in order from lowest expansivity (expands the least) to highest expansivity (expands the most).

3. Now let’s connect your ranking to real-world design choices. Answer these questions in your notebook

a. Bridges and Railway Tracks (Long Structures): Why is steel (or iron) often chosen for massive structures like railway tracks and long bridges, even though it still expands? What problem would arise if a metal with a very high expansivity was used for a long bridge without proper allowances for expansion?

b. Cooking Utensils (Pots and Pans): When choosing metals for the base of high-quality cooking pots and pans, engineers consider thermal expansion. Would you want a metal with very high expansivity or lower expansivity for the base of a good cooking pot? Explain your reasoning.

c. Bimetallic Strips (Smart Devices): You might recall that bimetallic strips rely on two different metals bending when heated. Looking at the table, which two metals from the list would be the best choices to create a bimetallic strip that would show the most significant bend for a given temperature change? Explain why you chose those specific two metals.

d. General Construction Advice (Accra’s Climate): Imagine you are an engineer advising a company building a large metal-framed building in Accra, Ghana, where temperatures can vary significantly between hot days and cooler nights. What general advice would you give them about considering thermal expansion when selecting and installing different metal components? Why is this understanding so critical for safe and durable construction?

Activity 2.5 Calculating Thermal Expansions

Study the worked examples carefully before attempting the sample questions that follow.

Worked Example 1

A steel railway track is 10 metres long at 20 °C. If the temperature rises to 45 °C on a sunny day, what will be its new length? (The coefficient of linear expansion for steel is 1.2 × 10⁻⁵°C⁻¹)

Step 1 - Identify the Given Values Original length (l₁) = 10 m Initial temperature (Tᵢ) = 20 °C Final temperature (T_(f)) = 45 °C Coefficient of linear expansion (α)= 1.2 × 10⁻⁵Step 2 - Introduce the formula for new length l₂ = l₁(1+ α ∆ θ)

Step 3 - Substitute the given values and calculate l₂ = 10 (1 + 1.2 × 10⁻⁵× (45 − 20)) l₂ = 10.003 m

Worked Example 2

A rectangular aluminium roof sheet has an area of 5 m²at 25 °C. If the temperature of the sheet rises to 65 ∘°C under the strong sun, what will be its new area? (The coefficient of linear expansion for aluminium=2.3 × 10⁻⁵°C⁻¹

Step 1 - Identify the Given Values Original area (A₀) = 5 m² Initial temperature (Tᵢ) = 25 °C Final temperature (T_(f)) = 65 °C Coefficient of linear expansion for aluminium (α)

Step 2 - Calculate the Coefficient of Area Expansion β = 2α β = 2 × 2.3 × 10⁻⁵°C⁻¹β = 4.6 × 10⁻⁵°C⁻¹Step 3 - Introduce the formula for new length A₂ = A₁(1+ β ∆ θ)

Step 4 - Substitute the given values and calculate A₂ = 5(1 + (4.6 × 10⁻⁵× (65 − 25)) A₂ = 5.0092 m²Worked Example 3 A car’s steel fuel tank is filled with 50 litres of petrol at 22 °C. If the temperature of the petrol rises to 38 °C during the day, how much petrol will overflow from the tank? (Assume the tank itself does not expand significantly. The coefficient of volume expansion for petrol is 9.5 × 10⁻⁴°C⁻¹) Step-by-Step Solution

Step 1 - Identify the Given Values Original volume of petrol (V₀) = 50 L Initial temperature (Tᵢ) = 22 °C Final temperature (T_(f)) = 38 °C Coefficient of volume expansion for petrol γ = 9.5 × 10⁻⁴°C⁻¹Step 2 - Introduce the formula for new length V₂ = V₁(1+ γθ)

Step 3 - Make the change in volume the subject V₂ − V₁ = V₁ γθ

Step 4 - Substitute the given values and calculate V₂ − V₁ = 50 × 9.5 × 10⁻⁴× (38 − 22)) V₂ − V₁ = 0.76 L Practice Problems Now, using the worked example as a guide, solve the following problems individually or in groups.

1. An overhead copper power cable is 500 metres long on a cool Harmattan morning at 15 ∘C. If the temperature in the afternoon rises to 35 °C, by how much does the cable’s length increase? (linear expansitivity of copper = 1.7 × 10⁻⁵°C⁻¹)

2. A square glass window pane (made of ordinary glass) has sides of 1.5 metres at 20 ∘C. What will its area be if the temperature drops to 0∘C on a cold night? (Note: expansion can also be contraction!) (linear expansitivity of copper of glass = 3.3 × 10⁻⁶°C⁻¹)

Activity 2.6 Revision on Thermometric Substances, Thermometers & Expansivities Objective: Refresh your understanding of thermometric substances and their characteristics, features and uses of different types of thermometers, and the concepts of linear, area, and volume expansivities including how to calculate them.

What you need

1. Notebook or paper and pen/pencil

2. Calculator (optional)

3. Access to previously learned notes or resources for reference (if needed) What to do

1. Write brief explanations for these topics

a. What is a thermometric substance?

b. Characteristics of common thermometric substances.

c. Features and uses of different types of thermometers (e.g., mercury, alcohol, gas thermometers).

2 Write what you remember about

a. Linear expansivity

b. Area expansivity

c. Volume expansivity

3. Using data or examples from your notes or studies, calculate at least one of each kind of expansivity (linear, area, volume) for metals or other materials you know.

4. Answer these questions in your own words

a. Why would you choose one thermometric substance over another in making a thermometer?

b. How are linear, area, and volume expansions related?

c. Why is understanding expansivity important in real-world applications like engineering or construction?

1. A farmer stores petrol in a sealed steel tank during the Harmattan season when temperatures are around 15 °C. Explain what precautions should be taken when the temperature rises to 40 °C, considering the expansion of both the tank and the petrol (you may wish to research these coefficients of expansion).

2. Two cooking pots are made of different metals: aluminium and stainless steel. Both are used in the same kitchen environment. Compare and justify which pot will be more durable against thermal fatigue when used repeatedly for cooking and cooling.

3. A bimetallic thermostat uses brass and steel strips bonded together. Explain why these metals are chosen and predict what would happen if two metals with very similar expansion rates were used instead.

4. A steel railway track is 30 m long at 15 °C. The maximum temperature in the region can rise to 45 °C.

a. Calculate the increase in length of the track. (Coefficient of linear expansion for steel, α = 1.2 × 10⁻⁵°C–¹)

b. Suggest why engineers allow expansion gaps between rails and calculate the minimum gap required if two consecutive rails are joined end to end.