I seem to remember from high school physics that the outer to inner diameter ratio determines whether or not the inner diameter will increase or decrease upon heating.

Is this true, or do they both increase linearly with temperature?

3/3/2008 2:24:23 PM

If I had to guess, the actual expansion should be somewhere in-between of the inner and outter diameter. As the metal heats up all the metal there-in will try to expand. But the inner and outter are connected to each other, so neither will be happy. The outter will expand less than it wants to and the inner will expand more than it wants to.

3/3/2008 2:45:29 PM

i may be wrong on this, but I believe you're correct stallion. I think its a ratio because the expansion of the ring is proportional to the amount of material it has in a certain direction. A normal ring with a small thickness doesnt have a large amount of material in the thickness direction, so the material will only get a little bit thicker (and it will expand in both direction, so really only half of the expansion makes up for the "closure". But the expansion of the whole ring is a function of the circumference (I think), which is generally much larger than the thickness, and as it expands, the whole ring "grows".

I'm sure theres some ratio that it has to be met. A quick paper calculation says that the thickness has to be = circumference/pi for the thermal expansion in the thickness direction to match the expansion in the circumferential direction. This was based on a 2-D ring, so I dont know how a 3-D on would work. But also, keep in mind a penny with a 1 mm hole would probably be about right so the thickness of the ring = circumference/pi, and normally "rings" arent really this thick.



[Edited on March 3, 2008 at 7:20 PM. Reason : also, this is assuming the coefficient of thermal expansion doesnt depend on geometry/direction]

3/3/2008 7:16:24 PM

wat?

if it's uniformly heated the end result should be a uniform scaling of the original shape.

3/4/2008 9:35:54 AM

I thought the question was how much, not how.

3/4/2008 12:26:33 PM

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thexp2.html#c2

3/4/2008 12:57:50 PM

if you run a stuck jar under hot water, the lid expands so it's easier to open.

3/4/2008 1:19:48 PM

yeah, i fucked it up. i was trying to open up the ring and essentially treat it like a rectangle, and the geometry isnt the same at all...

you have to split the circle into infinitely thin slices to treat it that way and when you do that the thickness expansion is some percentage of zero. the thickness increases as a whole, but only because the outer diameter "slice" expands more than the inner diameter.

Oddly enough, on a message board, some professor from Canada was arguing like a motherfucker that the ring thickness shrinks because volume is constant during thermal expansion just like if you stretched the ring out...

[Edited on March 5, 2008 at 2:18 AM. Reason : i haz seen the error of my ways]

3/5/2008 1:55:38 AM

That Canadian "professor" probably argued like a motherfucker that the Plane on a treadmill would never take off, as well.

Saying that volume stays constant during thermal expansion is retarded. Just look at the goddamn word. Thermal expansion. Does the volume of a gas stay constant when you heat it? There's some fools out there.

3/5/2008 2:56:09 AM

the volume of a gas will stay constant when you heat it if you keep it in a rigid container... just saying

[Edited on March 5, 2008 at 9:56 AM. Reason : ]

3/5/2008 9:56:31 AM

The plane will not take off if placed on an expanding ring.

3/5/2008 9:57:08 AM

^^^ it can, the pressure will just increase

3/5/2008 10:09:56 AM

Quote :

"if you run a stuck jar under hot water, the lid expands so it's easier to open."

Only if you run the lid under the water..... don't try running the jar under the water...

Just saying...

3/8/2008 12:53:45 AM

well the metal lid would have a higher coefficient of thermal expansion than the glass so it should help overall.

3/8/2008 2:29:10 AM

unless its one of those newfangled plastic lids... damn plastic to hell!

3/9/2008 11:25:17 AM

then it will melt off

3/9/2008 11:36:35 AM

Look! I has crafted this incredibly novel and environmentally friendly PPG lid!


LOL

3/9/2008 4:28:04 PM

JESUS FUCK

I miss college when I wondered about shit like this.

NEVER GRADUATE

NEVER GET A JOB

STAY IN SCHOOL FOREVER IF YOU CAN [/rant]

3/9/2008 9:24:59 PM

^X5

unless of course it's a jar of something really cold, where running hot water over it runs the risk of cracking the glass.

3/10/2008 9:58:10 AM