hopp@nbs-amrf.UUCP (Ted Hopp) (11/07/85)
Regarding my answer to the question about holes in metal being heated, Dan Levy (article <541@ttrdc.UUCP>) wonders about my gedanken experiment of watching the "hole" when it is filled (i.e., when the hole isn't there): > Isn't this begging the question? Suppose that internal forces/stresses > developed as a result of the expansion process. (This happens, for > example, with ordinary glass when it is heated, often resulting in > shattering [BTW, can anyone tell why it is that ordinary glass will > break when heated, but the same glass was successfully cooled into that > shape from a molten blob or sheet?].) Anyhow, some glasses, like Pyrex, > are much less subject to this since they expand much less when heated than > ordinary glass. The internal forces would constrain the "filler" piece > of material to be a slightly different shape when an integral part of the > whole than if heated by itself. This is beginning to sound like it should be net.physics. In the real world, you are right. There are combinations of materials, geometries, and heating processes for which a hole will end up smaller after heating even when the total volume of the material is larger. (I.e., I'm not even allowing those wierd materials [no one is allowed to mention water at freezing] that get smaller as they heat.) The effects I am thinking about are indeed caused by internal stresses, primarily a result of the material not being in thermal equilibrium as it is heated. In the puzzle world, though, one must assume that objects and processes are in some sense "ideal". To me, this meant that heating is uniform throughout the material at all times and that the material is homogeneous and isotropic (there is no preferred direction of expansion). The condition on the material is easy to accept; the condition on the heating process is sort of implied when the material was stated to be metal (known for its high thermal conductivity). The main reason glass shatters when heated is because thermal gradients cause uneven expansion. Forces are highest where the temperature gradient is highest. Rapid cooling can be just as bad as rapid heating - try touching a hot lightbulb with a cold wet cloth. (But be wearing gloves and safety glasses! Better yet, don't do it, just take my word for it. I did it once by accident when cleaning an oven.) A dramatic example of how important the heating/cooling process can be is in how large telescope mirrors are made. After the glass is poured, it is cooled extremely slowly. It can require many months for the glass to cool to room temperature. This is done so slowly just to prevent the glass from cracking due to stresses due to thermal gradients. Anyway, a perfectly homogeneous, isotropic, infinite thermal conductivity, positive thermal coefficient material (hope I have them all) with a hole in it will have a larger hole at higher temperatures. Almost all run-of- the-mill metals (cast iron, aluminum, etc.) will show the same behavior in the real world. -- Ted Hopp {seismo,umcp-cs}!nbs-amrf!hopp