# Thermal Expansion Question **URL:** \ **Category:** Factual Questions\ **Created:** [March 5, 2004, 9:52pm UTC](https://boards.straightdope.com/t/thermal-expansion-question/232773 "2004-03-05T21:52:44Z")\ **Posts on this page:** 10\ **Page:** 1
**Author:** ![Earthling](https://avatars.discourse-cdn.com/v4/letter/e/90db22/32.png) [@Earthling](https://boards.straightdope.com/u/Earthling)\ **Post date:** [March 5, 2004, 9:52pm UTC](https://boards.straightdope.com/t/thermal-expansion-question/232773/1 "2004-03-05T21:52:44Z")
Imagine that you have a cylinder with inside diameter of x, and a solid rod of the same material and length but of diameter x – 0.002" (or a dimension that’s just small enough) so that it barely slips into the cylinder. Now, when you heat the assemblage up, does it get tighter, because the cylinder expands from the material’s center (halfway between the inside and outside diameters), or does it get looser because everything expands from their common center of gravity? I realize this may sounds suspiciously like a homework question, but no, it’s just something I’ve been thinking about for a while but can’t figure out. ---
**Author:** ![hajario](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hajario/32/171_2.png) [@hajario](https://boards.straightdope.com/u/hajario)\ **Post date:** [March 5, 2004, 9:59pm UTC](https://boards.straightdope.com/t/thermal-expansion-question/232773/2 "2004-03-05T21:59:24Z")
It gets tighter. The volume of each shape will increase. Haj ---
**Author:** ![ElvisL1ves](https://avatars.discourse-cdn.com/v4/letter/e/5daacb/32.png) [@ElvisL1ves](https://boards.straightdope.com/u/ElvisL1ves)\ **Post date:** [March 5, 2004, 10:06pm UTC](https://boards.straightdope.com/t/thermal-expansion-question/232773/3 "2004-03-05T22:06:34Z")
If the 2 pieces are made from the same material, and both reach the same temperature over their entire volumes, they’ll actually stay loose. They’ll both expand from their centers of mass, to use your visualization. The expansion of the solid rod is easy to visualize; it grows by the same percentage in any linear dimension. But the hollow cylinder will grow, too. Although it’s true that its volume will increase, its ID doesn’t get tighter unless its OD is somehow constrained. Think of cutting a slit lengthwise and unwrapping it so it’s a rectangle. Heat it up and it expands in all directions by an equal percentage. Now wrap it back into a cylinder, still hot, so that its width becomes the new circumference of the cylinder. Divide by pi and you’ll see that both ID and OD have grown by the same percentage (the math gets more complicated if the wall is thick compared to the radius, though). ---
**Author:** ![billy](https://avatars.discourse-cdn.com/v4/letter/b/ecd19e/32.png) [@billy](https://boards.straightdope.com/u/billy)\ **Post date:** [March 5, 2004, 10:23pm UTC](https://boards.straightdope.com/t/thermal-expansion-question/232773/4 "2004-03-05T22:23:39Z")
> [@hajario](#): > > It gets tighter. The volume of each shape will increase. > > Haj Nope. The holes in the objects will get larger just as the over all object does. And because the holes are larger than the rods going through them, the holes will have an absolute expansion larger than the rods will so they will actually get looser. ---
**Author:** ![Phage](https://avatars.discourse-cdn.com/v4/letter/p/a4c791/32.png) [@Phage](https://boards.straightdope.com/u/Phage)\ **Post date:** [March 5, 2004, 10:59pm UTC](https://boards.straightdope.com/t/thermal-expansion-question/232773/5 "2004-03-05T22:59:36Z")
Ok, we have tighter, the same, and looser as answers… Can anyone tell me what happens when a car’s engine gets too hot? ---
**Author:** ![hajario](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hajario/32/171_2.png) [@hajario](https://boards.straightdope.com/u/hajario)\ **Post date:** [March 5, 2004, 11:06pm UTC](https://boards.straightdope.com/t/thermal-expansion-question/232773/6 "2004-03-05T23:06:48Z")
> [@billy](#): > > Nope. The holes in the objects will get larger just as the over all object does. And because the holes are larger than the rods going through them, the holes will have an absolute expansion larger than the rods will so they will actually get looser. I just pulled out an old text book and I am ashamed to say that **billy** is correct. Apologies Haj ---
**Author:** ![MadScientistMatt](https://avatars.discourse-cdn.com/v4/letter/m/bc8723/32.png) [@MadScientistMatt](https://boards.straightdope.com/u/MadScientistMatt)\ **Post date:** [March 5, 2004, 11:17pm UTC](https://boards.straightdope.com/t/thermal-expansion-question/232773/7 "2004-03-05T23:17:06Z")
**Billy** is correct - the clearance distance will increase along with all the other dimensions. Another effect to watch for is that if you heated it in an oven, the temperature of the outer cylinder would increase faster than the temperature of the inner cylinder, making the clearance temporarily even larger. ---
**Author:** ![Strainger](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/strainger/32/244_2.png) [@Strainger](https://boards.straightdope.com/u/Strainger)\ **Post date:** [March 5, 2004, 11:54pm UTC](https://boards.straightdope.com/t/thermal-expansion-question/232773/8 "2004-03-05T23:54:59Z")
To add some quantitative information, the change in hole diameter (inner or out) due to change in temperature is: [symbol]D[/symbol]D=[symbol]a[/symbol]D[symbol]D[/symbol]T where [symbol]a[/symbol] is the coefficient of thermal expansion for the material. So for **Earthling** ’s example, the radial gap is going to increase by the amount 0.001[symbol]a[/symbol][symbol]D[/symbol]T. As further proof of the hole diameter increasing when heated, imagine a flat plate heated up to a given temperature. You’ll have unform expansion, of course. Now, cut out a disk in the center of the plate with an infinitely thin blade, but leave the disk inside the hole and heat it up again. Do you end up with thermal stresses at the interface between the hole and disk? Off course not. The hole and the disk expand at the same rate. Got that proof from _Marks Handbook for Mechanical Engineers_. ---
**Author:** ![zut](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/zut/32/2875_2.png) [@zut](https://boards.straightdope.com/u/zut)\ **Post date:** [March 6, 2004, 12:07am UTC](https://boards.straightdope.com/t/thermal-expansion-question/232773/9 "2004-03-06T00:07:46Z")
> [@Phage](#): > > Can anyone tell me what happens when a car’s engine gets too hot? Different problem altogether. Engines, in general, are made of different materials with different coefficients of thermal expansion. More importantly, temperature change is _not_ uniform all over the engine (it’s hotter in the cylinder, right?) and different places are constrained differently (say, near head bolts vs. at the periphery). So best I can do is tell you that too hot = bad, since the entire engine will expand in non-uniform ways. ---
**Author:** ![LSLGuy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lslguy/32/5813_2.png) [@LSLGuy](https://boards.straightdope.com/u/LSLGuy)\ **Post date:** [March 6, 2004, 2:12am UTC](https://boards.straightdope.com/t/thermal-expansion-question/232773/10 "2004-03-06T02:12:06Z")
In a piston engine, the pistons are heated more than the cylinders (or at least have less effective cooling), or are made from a more expansive material, or both. So the usual failure mode of an overheated piston engine is that the pistons “swell” relative to the cylinders until the clearance becomes zero. Then it seizes. Looked at in more detail, a few minutes before the clearances would have gotten to zero, a piston ring will usually start to stick, which produces a burr on the cylinder wall and now we have metal-to-metal unlubricated contact, a local hotspot, and the whole failure cascade starts within a few seconds.