Thermal Expansion linear vs area expansion

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Homework Help Overview

The discussion revolves around the topic of thermal expansion, specifically comparing linear expansion to area expansion. The original poster questions the relationship between the area coefficient of expansion and the linear coefficient of expansion.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the concept of thermal expansion by considering a square object and applying linear expansion to its dimensions to derive an expression for the change in area. Questions arise regarding the implications of changes in side length on the area and whether the area change can be simplified.

Discussion Status

The discussion has progressed with participants providing insights into the mathematical relationships involved. Some participants have confirmed the reasoning behind the increase in area due to changes in side length, while others continue to seek clarity on the original question posed by the poster.

Contextual Notes

Participants are working within the framework of thermal expansion principles and are considering the implications of coefficients of expansion in their calculations. There is an emphasis on understanding the relationship between linear and area expansion coefficients.

Searay330
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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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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?
 
im not sure the change in area would be equal to the new L2 and that is the only dimension that changes
 
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?
 
its increased by 2(αLΔT) one for each side
 
Searay330 said:
its increased by 2(αLΔT) one for each side
Right. Does that answer your original question?
 
yes
 

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