Thermal Expansion linear vs area expansion

In summary, the conversation discusses the concept of thermal expansion for linear vs area. The question is raised about why the area coefficient of expansion is equal to 2 times the linear coefficient of expansion. An example is given to demonstrate this concept and it is concluded that the area coefficient of expansion is indeed equal to 2 times the linear coefficient of expansion.
  • #1
Searay330
20
1
Member warned to use the formatting template for homework posts.
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this is a picture of my notes for thermal expansion for linear vs area.
my question is why does the area coefficient of expansion for the area = 2(liner coefficient of expansion).
any insight would be appreciated.
 
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  • #2
As an example to ponder, consider an object with a flat, square surface that is L units of length on each side. Apply the linear expansion concept to each dimension and work out an expression for the change in area. Then consider that the coefficient of linear expansion ##\alpha## is typically on the order of a few parts per million per degree C. Is there an obvious simplification?
 
  • #3
im not sure the change in area would be equal to the new L2 and that is the only dimension that changes
 
  • #4
Searay330 said:
im not sure the change in area would be equal to the new L2 and that is the only dimension that changes
No, the change in area would not equal L2.
If the original side of the square is L, the original area is L2.
If the new side length is ##L+\alpha L\Delta T##, what is new area? How much has the area increased by?
 
  • #5
its increased by 2(αLΔT) one for each side
 
  • #6
Searay330 said:
its increased by 2(αLΔT) one for each side
Right. Does that answer your original question?
 
  • #7
yes
 

What is thermal expansion?

Thermal expansion is the phenomenon in which a material expands or contracts in response to changes in temperature. This occurs because as temperature increases, the particles within a material gain kinetic energy and vibrate at a higher frequency, causing the material to expand. Similarly, as temperature decreases, the particles lose kinetic energy and vibrate at a lower frequency, causing the material to contract.

What is linear expansion?

Linear expansion is a type of thermal expansion in which a material expands or contracts in one dimension (length) due to changes in temperature. The change in length is directly proportional to the change in temperature and is described by the linear expansion coefficient of the material.

What is area expansion?

Area expansion is a type of thermal expansion in which a material expands or contracts in two dimensions (length and width) due to changes in temperature. The change in area is directly proportional to the change in temperature and is described by the area expansion coefficient of the material.

What is the difference between linear and area expansion?

The main difference between linear and area expansion is the dimension in which the material expands or contracts. Linear expansion occurs in one dimension, while area expansion occurs in two dimensions. Additionally, the equations used to calculate the change in length and area differ, with linear expansion using the linear expansion coefficient and area expansion using the area expansion coefficient.

Why is it important to consider thermal expansion in engineering and construction?

Thermal expansion is an important factor to consider in engineering and construction because it can cause materials to expand or contract, potentially leading to structural damage or failure. It is especially important to consider in large structures or structures made of different materials, as the different rates of expansion can cause stress and strain on the structure. By understanding thermal expansion, engineers and construction workers can design and build structures that can withstand these changes in temperature.

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