Does Heat Cause Area Expansion? Understanding the Expansion of Materials

AI Thread Summary
Heating an aluminum plate causes all dimensions, including the square hole, to expand due to thermal expansion. The formula δL/L = β*δT indicates that linear dimensions increase proportionally to temperature change. As the sides of the hole expand, the overall area of the hole increases rather than decreases. The confusion arises from misunderstanding that the expansion affects both the material surrounding the hole and the hole itself. Therefore, the correct conclusion is that the area of the hole becomes larger when the aluminum plate is heated.
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Homework Statement



This is a question from my physics book, i don't understand its solution.

Consider a square hole in an aluminum plate (2D) . If this block is heated,
will this hole become smaller or larger ?

Homework Equations



δL/L = β*δT


The Attempt at a Solution



As each of the side of the block expands (some a lttle, while the longer sides more) thus the area decreases.

But, the answer as given by the book is that the area would increase.
Can anyone help me understand this ?
 
Physics news on Phys.org
All linear dimensions will expand by the same factor, including the hole.
 

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