Volume Expansion of Solid and Hollow Objects at Different Temperatures

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When comparing solid and hollow objects made of the same material and dimensions, both experience volume expansion when heated. The solid object has a greater initial volume than the hollow one, leading to more overall expansion. However, the coefficients of volume expansion are the same due to the identical material. The discussion raises questions about whether the hollow object's hole expands similarly to the solid body's dimensions. Ultimately, it suggests that both objects may appear to expand similarly from the outside despite their structural differences.
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Let's say you have two bodies which are made of the same material and have the same external dimensions and appearance, but one is solid and the other is hollow. You increase their temperature, now is the overall volume expansion the same or different?

What do you think?
 
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hi failexam! :wink:

tell us what you think, and then we'll comment! :smile:
 
The two bodies are made of the same material, so they must have the coefficients of volume expansion. Also, they have the same external dimensions.

But, one body is solid and the other is hollow. So, the solid body has greater volume than the hollow body.

Volume expansion depends on the coefficient of volume expansion, initial volume and external dimensions, so the solid body will expand more than the hollow body.

What do you think? :confused:
 
failexam said:
Volume expansion depends on the coefficient of volume expansion, initial volume and external dimensions, so the solid body will expand more than the hollow body.

yes :smile:, in the same sense that a large solid body will expand more than a small solid body …

but does that necessarily mean that a solid body will expand to a bigger diameter than the originally-same-diameter body?

what do you think happens to the hole?

what happens in the easy case of a hollow cube whose hole is one-third the diameter of the whole cube (so the hollow cube is 8 cubes joined together)? :wink:​
 
(as an aside, wouldn't that have to be 26 cubes? Nine on "top", nine on "bottom", and 8 between them? Basically it should be the number of cubes visible on the exterior of a Rubiks cube)

Anyway, my feeling is that the hollow and solid objects should expand the same amount--at least in appearances, from the outside.
 
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