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Today, we will explore linear expansion, which is the change in length of a solid when its temperature changes. How many of you have noticed that when a metal object like a spoon gets hot, it feels longer?
I think I have! Does it actually get longer?
Yes, it does! This change can be measured using the formula ΔL = αL₀ΔT. Can anyone tell me what the symbols in this formula represent?
ΔL is the change in length, right?
Correct! And L₀ represents the original length. How about α?
It’s the coefficient of linear expansion!
Exactly! This coefficient tells us how much a material expands per degree of temperature increase.
What happens if the temperature decreases? Does it shrink back?
Good question! Yes, as the temperature decreases, the material shrinks back to its original length.
Let's look at an example. Say we have a metal rod 3 meters long at 20°C, and we heat it to 100°C with a coefficient of linear expansion α at 1.5 × 10⁻⁵ °C⁻¹. Who can help me calculate the change in length?
I can! We can use the formula ΔL = αL₀ΔT.
That's right! Substituting the values, what do we get?
ΔL = (1.5 × 10⁻⁵) × 3 × (100 - 20) = 0.0036 m!
Excellent! So the rod expands by 3.6 mm. Always remember, in engineering, we need to consider these changes!
What if the rod was a different material with a different α?
That's a great point! Different materials expand at different rates. Knowing the coefficient is crucial for accurate calculations.
The effect of temperature on the length of a solid.
Measures how much a material expands per degree increase in temperature.
Understanding how to compute length change using the formula ΔL = αL₀ΔT.
When metals get hot, they grow tall, remember to measure, or risk a fall.
Once a metal rod was heated by the sun, it expanded so much, it thought it was done! But then cool air came to keep it tame, it shrank back to its length, just the same.
L.A.T: Length, Area, Temperature - to remember the aspects of thermal expansion.
C.L.E: Coefficient, Length, Expansion - to recall what's essential for linear expansion.
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What is Linear Expansion?
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Formula for Linear Expansion?
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What does α represent?
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What happens to solids when cooled?
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The increase in length of a solid when its temperature rises.
A material property that indicates the fractional change in length per degree of temperature change.
Change in length of the solid.
Original length of the solid.
Change in temperature (in °C).
Linear expansion refers to the change in length of a solid due to a temperature change, described by a specific equation.
In this section, the concept of linear expansion is introduced, emphasizing its formula, the coefficient of linear expansion, and practical examples demonstrating how it is calculated. It is a fundamental concept in thermal expansion that plays a crucial role in materials engineering and science.
Linear expansion refers to the phenomenon where the length of a solid increases in response to a rise in temperature. This section delves into the concept using the formula:
ΔL = αL₀ΔT
Where:
The coefficient of linear expansion (α) is a material property that quantifies how much a material expands per degree change in temperature. The example provided calculates the change in length of a metal rod when it is heated from an initial temperature of 20°C to 100°C, illustrating the practical application of the formula.
Understanding linear expansion is essential in engineering fields, where temperature changes in materials must be considered to avoid structural failures.