Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83; site ttrdc.UUCP Path: utzoo!watmath!clyde!burl!ulysses!mhuxr!mhuxt!houxm!ihnp4!mgnetp!ltuxa!ttrdc!levy From: levy@ttrdc.UUCP (Daniel R. Levy) Newsgroups: net.puzzle,net.math Subject: Re: Re: Polar Bear Problem Sequel Message-ID: <541@ttrdc.UUCP> Date: Thu, 31-Oct-85 17:58:54 EST Article-I.D.: ttrdc.541 Posted: Thu Oct 31 17:58:54 1985 Date-Received: Sat, 2-Nov-85 05:29:58 EST References: <361@proper.UUCP> <367@faron.UUCP> <10755@ucbvax.ARPA> <42@nbs-amrf.UUCP> Distribution: net Organization: AT&T, Computer Systems Division, Skokie, IL Lines: 34 Xref: watmath net.puzzle:1118 net.math:2450 In article <42@nbs-amrf.UUCP>, hopp@nbs-amrf.UUCP (Ted Hopp) writes: >> If you have a piece of metal >> with a spherical hole in it, does the hole expand, contract, or remain >> the same when the metal is heated? What about a square hole? I don't >> know the answer! >> ...ranjit bhatnagar > >Actually, the hole (spherical, square, circular, or whatever) will >expand. Imagine heating the metal that filled the hole when the metal >was cool while you are heating the metal with the hole. The "filler" >will fit back into the hole when both are hot. Since the filler >chunk expanded (being metal), the hole must have expanded. As to >why the filler should fit back in, imagine heating the metal plus >filler without separating the filler - if it isn't going to fit in >when heated separately, why does it exactly fill where the hole would >have been? 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. Just ramblin' on... -- ------------------------------- Disclaimer: The views contained herein are | dan levy | yvel nad | my own and are not at all those of my em- | an engihacker @ | ployer or the administrator of any computer | at&t computer systems division | upon which I may hack. | skokie, illinois | -------------------------------- Path: ..!ihnp4!ttrdc!levy