# Thermal expansion: the amount of material expanding is "irrelevant"?

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1. Feb 15, 2015

Hello everyone!

First time asking a question here, go easy on me!!
I am a first year Mech-Eng student in Ireland, and I need some guidance from one of the amazing brains here at physicsforums.

I am told by my thermofluids lecturer that in thermal expansion, the amount of material expanding is "irrelevant", and will expand the same amount. Allow me to explain this better;

She says that if you take a 100mm diameter solid steel cylinder, and a steel pipe with an external diameter of 100mm, but with a gauge thickness of, say 5mm, then if both are heated the same, the amount each specimen will expand linearly will be the same....i.e the final external diameter will be the same.

I really hope I am just being thick, because my lecturer should know this stuff, but it doesn't make sense to me. I feel that if a solid cylinder of steel is heated, it can only expand outwards, increasing outwards linearly and cubically. If the same heat is applied to a hollow pipe of the same material, I feel the hollow center would allow for some inward expansion, making the final values for diametric expansion different... I also imagine the more material there is, the greater the total expansion will be.....i.e; if there are 5 iron atoms side by side and they expand uniformly, won't that be a smaller amount of linear expansion than if there were 5,000,000 atoms side by side???

I hope I explained that well enough. This lecturer is great, and if this sounds totally nuts, she most likely misunderstood my goofy, confusing questions!

who is right? And could a resident genius please elaborate?

Thanks very much

T

2. Feb 15, 2015

### Staff: Mentor

Inwards expansion means the inner radius would decrease - you would have to compress the material there (because your material is solid, not liquid).
What really happens is a linear expansion of all distances between atoms, which means the whole structure expands by some constant factor, including the inner radius.

The absolute linear expansion will depend on the length you consider, sure. A chain of 1 million atoms will expand 1000 times more than a chain of 1000 atoms - but the relative expansion stays the same because the first chain is also 1000 times longer.

3. Feb 15, 2015

Awesome, thank you so much for the reply.
I understand what you said about the internal radius, but in the example I gave, would the two specimens' final diameter still be the same??
..a solid steel cylinder of 100mm outer diameter, say 200mm long, heated to the same temp as a 200mm section of 5mm gauge steel pipe also of outer diameter 100mm.... why can't I understand this???!

thanks for your time though, MFB

4. Feb 15, 2015

### Staff: Mentor

Yes they would be the same.
All distances between the atoms increase by the same ratio, so the outer diameter increases by the same factor, and radius is proportional to this diameter.

5. Feb 15, 2015

### Bystander

... can be thought of as a "nesting" of close fitting pipes/tubes about a small solid rod, and consider the elements of the "nest" individually.

6. Feb 15, 2015

Thank you very much for your knowledge, MFB, and for the explanation. it makes a lot more sense. but it still hasn't clicked!! Bystander, dude, I totally wish I could understand what you mean, and thanks for the input. But I may need to have it explained to me in the same manner you might explain it to somebody who just received a blow to the head. Don't know why I can't digest this!!

If we consider the internal and external diameters of the pipe as chains of atoms, are the inner atoms spaced the same distance apart as the outer ones?? because if there are simply more atoms in the solid cylinder than in the hollow tube, all spaced as evenly as each other, surely the atoms of the solid cylinder would be spaced further apart to allow the external atoms to make room for .....wait....does that mean that the outer atoms prevent the shape from expanding more than....aaah what?

the worst part is I have another question, about something else unrelated!

7. Feb 15, 2015

### Staff: Mentor

All lines in the material grow by the same percentage. One of these lines is the circumference. Whether the cylinder is solid or hollow, each circumferential hoop grows by the same %.

Chet

8. Feb 15, 2015