# Some ‘splainin to do!

There was, if I am not mistaken, an episode of I Love Lucy wherein Lucy manages to get her head stuck in a metal teakettle. Ethel jokingly (I hope!) suggests that she put her head in the oven to heat up the metal so it will expand and she can fit her head out. A clever idea, not counting the fact that it would have unfortunate side effects for Lucy!

But we shouldn’t be so convinced it would work. Consider a piece of sheet metal with a circular hole punched out. Heated, the metal expands. The hole will either get larger or smaller – does the overall expansion cause the metal to expand away from the hole, or does the metal’s expansion force it into the space formerly occupied by the emptiness of the hole?

Or what if it’s not a circle? Does the shape of the hole make a difference?

I like to poll my students on this. The split is usually pretty even between the larger and smaller schools of thought, at least among those who haven’t had engineering classes that might have already told them the answer. The neat thing about science is that you don’t have to decide which school of thought to believe, and the numbers of people who think one way or another are absolutely irrelevant. Instead, you can check your idea against first principles and then check your check via experiment.

Here’s a hint. Think of the atoms of the material as though they were arranged in a neat grid. Thermal expansion makes the grid spacing larger. If there’s a gap in the grid, what happens to its size as the grid spacing increases?

And should you want to see the answer for yourself experimentally (you should!), I’ve found a site that actually has video of the experiment.

1. #1 Max Fagin
February 13, 2009

I’m going with larger. Thank you ENGS 24.

2. #2 HP
February 13, 2009

I blame the wide availability of plastics. Back in my day, if you had a glass jar with a metal lid, and the lid was stuck, you could run the lid of the jar under hot water for a minute or so, and it would pop right off.

Since Big Peanut Butter & Jelly went to plastics, today’s young people have no daily exposure to the thermal rate of expansion of metals.

Also, Ethel could’ve simply poured hot water from the tap over Lucy’s teapot helmet to expand it sufficiently without harming Lucy. We know from the radiator episode that Fred kept the building’s boiler plenty hot enough.

3. #3 mtc
February 14, 2009

The way to visualize it that makes sense to me is thinking of all the atoms around the edge of the hole. If the distance between those atoms has to increase, then the circumference of the circle they form has to increase, and the hole gets bigger.

4. #4 jth
February 14, 2009

I was originally going to go with Lucys head getting crushed into a walnut, but then I remembered my physics of the cosmos and the reason for the doppler shift.

5. #5 Robert
February 15, 2009

Lucy is still stuck as the size of the hole does not change. Of course, I could be wrong as I haven’t seen the video. I’ll save my explanation (when I come up with a coherent one) until after the coffee kicks in. Cheers.

6. #6 Flymises
February 15, 2009

Indeed, mtc.

I thought about it similarly: In order for the hole to get smaller, the atoms around the edge of the hole would have to be crushed together. Of course, this doesn’t make sense with expansion; the force of the atoms pushing against each other would surely cause an outward expansion.

Of course, I wasn’t confident with my reasoning until I saw the experiment (because all sorts of weird things can happen in Physics which we would never have thought of!)

7. #7 Robert
February 15, 2009

Having just watched the video after offering my opinion- there is only one possible conclusion- no thinking allowed before coffee.

8. #8 Laura
February 21, 2009

‘Twas a “Loving Cup” – a trophy.

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