9.2 - Thermal Expansion of Solids
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Interactive Audio Lesson
Listen to a student-teacher conversation explaining the topic in a relatable way.
Introduction to Thermal Expansion
🔒 Unlock Audio Lesson
Sign up and enroll to listen to this audio lesson
Good morning everyone! Today, we will discuss thermal expansion, which is how materials increase in size when we heat them. Can anyone tell me what happens to the particles inside a solid when it gets heated?
Do they move faster and spread out?
That's correct, Student_1! As solids heat up, their particles vibrate more vigorously and tend to move apart, leading to an increase in size. This leads us to linear expansion. Can anyone share what linear expansion might mean?
Isn't it when a solid's length increases?
Exactly, it relates to how the length of a solid changes with temperature. The formula for this is ΔL = αL0ΔT. Let’s break down what each term means.
So ΔL is the change in length, right? What about α?
Great question! α is the coefficient of linear expansion, which varies for different materials, indicating how much that material expands per degree Celsius. For instance, metals usually have higher α values. Think of the word 'expand' when you think of α—it's all about how far a material can stretch!
So do materials with a higher α expand more than those with a lower α?
Exactly! Excellent observation, Student_4. Types of materials affect this significantly. To summarize, thermal expansion is crucial in many engineering applications. Remember, α is about how much we 'expand'!
Area and Volumetric Expansion
🔒 Unlock Audio Lesson
Sign up and enroll to listen to this audio lesson
Now that we've discussed linear expansion, let's look at area expansion. Can anyone share what it means when a solid's area changes with temperature?
Does that mean it gets larger in two dimensions?
Absolutely! The formula for area expansion is ΔA = 2αA0ΔT. So if you know the original area and the temperature change, we can predict how the area will change. Why do you think it’s multiplied by 2?
Because it expands in both directions, like length and width?
Precisely! Well explained, Student_2. Now, what about volumetric expansion? The formula is ΔV = βV0ΔT. Can anyone tell me what β represents?
Is it the coefficient of volumetric expansion?
Correct! For most solids, β is approximately three times α. This means when you heat a solid, it increases in volume by a factor related to both area and linear changes. Let’s remember to use two and three times for area and volume, respectively!
Why is it three times for volume?
Great question! Think of it as how cubed all dimensions become when a solid is heated. Everything scales up! Any last questions before we summarize?
Examples of Expansion
🔒 Unlock Audio Lesson
Sign up and enroll to listen to this audio lesson
Let's look at a practical example of linear expansion to cement our understanding. If we have a metal rod of 3 meters heated from 20°C to 100°C with a coefficient of linear expansion of 1.5x10^-5° C⁻¹, how would we calculate the change in length?
We plug it into the formula!
Exactly! So, using ΔL = αL0ΔT, what is ΔL?
ΔL = (1.5×10−5)×3×(100−20) = 0.0036 m, which means it increases by 3.6 mm!
Spot on, Student_2! Let’s discuss why this is essential in engineering. Why do we care about expansion when designing structures like bridges?
Because if they don't account for it, they can crack or break, right?
You got it, Student_3! Engineers must include expansion joints to handle changes in temperature and prevent damage. Remember, thermal expansion is all around us, from railways to the hinges on doors!
Introduction & Overview
Read summaries of the section's main ideas at different levels of detail.
Quick Overview
Standard
This section outlines the concepts of linear, area, and volumetric expansion in solids, introducing relevant formulas and coefficients. It illustrates key points through examples like the expansion of a metal rod, emphasizing the practical implications of thermal expansion in everyday objects and engineering applications.
Detailed
Detailed Summary: Thermal Expansion of Solids
Introduction
Thermal expansion describes how materials change in size or volume in response to temperature changes. When a solid is heated, its particles move more vigorously, resulting in an increase in size typically measured in one, two, or three dimensions. The section specifically covers:
- Linear Expansion: Defined by the formula ΔL = αL0ΔT, where ΔL is the change in length, α is the coefficient of linear expansion, L0 is the original length, and ΔT is the change in temperature. This expression highlights how materials elongate with temperature increases.
- Coefficient of Linear Expansion: This coefficient is specific to each material, indicating how much it expands per degree Celsius. The relationship means materials with a higher α will expand more significantly when heated.
- Area and Volumetric Expansion: The formulas for area expansion (ΔA = 2αA0ΔT) and volumetric expansion (ΔV = βV0ΔT) illustrate how solids may also change in area and volume, respectively.
- Coefficient of Volumetric Expansion: It is roughly three times the coefficient of linear expansion, implying the geometric relationship between linear and volume changes.
Key Examples
- Example of Linear Expansion: A calculation is provided for a metal rod whose length changes with temperature, demonstrating the application of the linear expansion formula and yielding a concrete increase in measurement.
- The section implies a broader context to the impacts of thermal expansion in engineering and everyday scenarios, influencing design and functionality.
Youtube Videos
Audio Book
Dive deep into the subject with an immersive audiobook experience.
Linear Expansion
Chapter 1 of 5
🔒 Unlock Audio Chapter
Sign up and enroll to access the full audio experience
Chapter Content
The change in length of a solid when its temperature changes is termed linear expansion. It is given by the formula:
ΔL = αL0ΔT
Where:
○ ΔL = Change in length (in meters)
○ α = Coefficient of linear expansion (in per °C)
○ L0 = Original length of the solid (in meters)
○ ΔT = Change in temperature (in °C)
Detailed Explanation
Linear expansion describes how the length of a solid object changes as its temperature changes. When you heat a solid, the particles within it vibrate more vigorously, causing the object to stretch or lengthen. The formula for calculating the change in length is ΔL = αL0ΔT, where ΔL is the change in length, α is the coefficient of linear expansion specific to the material, L0 is the original length, and ΔT is the temperature change. For example, if a metal rod initially measures 2 meters and heats up by 50 degrees Celsius, you can calculate how much longer it becomes using this equation.
Examples & Analogies
Think of a metal ruler left outside on a hot summer day. As the sun heats the metal, it expands. If you measure its length before and after being in the sun, you'll notice it is slightly longer. This is due to linear expansion, a principle seen in various applications, like railroad tracks, which have gaps to allow for this expansion.
Coefficient of Linear Expansion
Chapter 2 of 5
🔒 Unlock Audio Chapter
Sign up and enroll to access the full audio experience
Chapter Content
The coefficient of linear expansion α is a property of the material and represents the fractional change in length per unit temperature change. Materials with high α expand more with a temperature increase.
Detailed Explanation
The coefficient of linear expansion (α) indicates how much a material expands per degree of temperature increase. Each material has its own unique coefficient, meaning some will expand more than others when subjected to the same temperature change. For example, metals generally have a higher coefficient compared to glass or wood. This property is crucial in designing structures and devices that rely on temperature variations so that they function correctly without damage.
Examples & Analogies
Consider the differences between a metal rod and a wooden stick when exposed to heat. If both are heated to the same temperature, the metal rod will expand more significantly than the wooden stick. This is why engineers choose materials carefully when constructing buildings, bridges, or even cookware; they need to account for how much each material will expand or contract with temperature changes.
Example of Linear Expansion
Chapter 3 of 5
🔒 Unlock Audio Chapter
Sign up and enroll to access the full audio experience
Chapter Content
A metal rod of length 3 m is heated from 20°C to 100°C. If the coefficient of linear expansion is 1.5×10−5 °C⁻¹, the change in length is:
ΔL = (1.5×10−5) × 3 × (100−20) = 0.0036 m
Hence, the length increases by 3.6 mm.
Detailed Explanation
In this example, we calculate the change in length (ΔL) of a metal rod. The rod starts at a length of 3 meters and is heated from 20°C to 100°C, a temperature increase of 80°C. Using the coefficient of linear expansion α = 1.5×10−5 °C⁻¹, we can apply the formula ΔL = αL0ΔT. Plugging in the values, we calculate that the rod expands by 0.0036 meters, which is equivalent to 3.6 mm or about the thickness of a dime. This succinctly illustrates how even seemingly small temperature changes can lead to measurable expansions.
Examples & Analogies
Imagine heating a metal soup spoon by leaving it in hot soup. As the spoon absorbs heat, it expands slightly. While this change is often unnoticed in everyday scenarios, it is critical in precise measurements and applications such as manufacturing or construction, where even minor length alterations can affect the overall function and safety.
Area Expansion
Chapter 4 of 5
🔒 Unlock Audio Chapter
Sign up and enroll to access the full audio experience
Chapter Content
The change in area of a solid when its temperature changes is given by:
ΔA = 2αA0ΔT
Where:
○ ΔA = Change in area (in m²)
○ A0 = Original area (in m²)
Detailed Explanation
Area expansion occurs when a two-dimensional object expands due to heat. The formula for area expansion is ΔA = 2αA0ΔT, where ΔA represents the change in area, A0 is the original area, α is the coefficient of linear expansion, and ΔT is the temperature change. This means that as the temperature of a solid increases, not only does its length increase, but its entire area does so proportionally, which can be significant in applications involving surfaces.
Examples & Analogies
Consider a metal sheet being used to cover a hot grill. As the sheet heats up, it expands not just in length, but also in width. If the area of the sheet is significant, this actual increase can affect its fit and placement. It's similar to how a balloon expands in all directions as the air inside warms up, showcasing area expansion.
Volumetric Expansion
Chapter 5 of 5
🔒 Unlock Audio Chapter
Sign up and enroll to access the full audio experience
Chapter Content
The change in volume of a solid when its temperature changes is given by:
ΔV = βV0ΔT
Where:
○ ΔV = Change in volume (in m³)
○ β = Coefficient of volumetric expansion (in per °C)
○ V0 = Original volume (in m³)
Detailed Explanation
Volumetric expansion describes the change in the volume of a solid as its temperature changes. The formula for volumetric expansion is ΔV = βV0ΔT, where ΔV is the change in volume, V0 is the original volume, and β (beta) is the coefficient of volumetric expansion. Generally, the volumetric expansion coefficient is about three times the linear expansion coefficient for most materials, indicating how solids not only stretch but also inflate in three dimensions when heated.
Examples & Analogies
To visualize volumetric expansion, think of a sealed bottle of soda left in the sun. As the temperature rises, the liquid inside expands slightly, increasing the pressure and potentially causing the bottle to burst if the temperature rises too high. Similarly, a hot soup pot full of water expands, which is why it should not be completely filled to the brim, as the volume increase from heating can lead to spills.
Key Concepts
-
Thermal Expansion: The increase in size or volume of a material when its temperature rises.
-
Linear Expansion: Change in length of a material due to temperature changes.
-
Area Expansion Formula: ΔA = 2αA0ΔT, showing area change with temperature.
-
Volumetric Expansion Formula: ΔV = βV0ΔT, illustrating how volume changes with heat.
Examples & Applications
A metal rod expands by 3.6 mm when heated from 20°C to 100°C, illustrating linear expansion.
A metal structure without expansion joints might crack due to temperature-induced expansion.
Memory Aids
Interactive tools to help you remember key concepts
Rhymes
When the heat arrives, materials expand, / Length, area, volume all increase at hand.
Stories
Imagine a metal rod resting in the sun, it starts to grow longer as it has some fun! As it heats, it stretches, a wondrous sight, reminding us of expansion, oh what a delight!
Memory Tools
Remember LEAP: Length (linear expansion), Area (Area expansion), and Volume (Volumetric expansion).
Acronyms
Use A.L.V for Area, Length, and Volume expansion to recall the three types.
Flash Cards
Glossary
- Thermal Expansion
The increase in size or volume of a substance when its temperature rises.
- Linear Expansion
The change in length of an object when its temperature changes.
- Coefficient of Linear Expansion (α)
A measure of how much a material’s length changes per degree of temperature change.
- Area Expansion
The change in area of an object with temperature change.
- Volumetric Expansion
The change in volume of an object when its temperature increases.
- Coefficient of Volumetric Expansion (β)
A property measuring how much a material's volume changes per degree of temperature change.
Reference links
Supplementary resources to enhance your learning experience.