alex@pluto.UUCP (Alex Orensteyn) (11/07/85)
I am not sure why such a simple question as heat-expansion of metal
deserves this extensive controversy and personal verbal abuse. I
think I know a little about this problem, so I shall try to clarify it
to the best of my ability.
1) First of all everybody who said that a hole in a piece of
metal would expand if that piece of metal were heated are quite
right, that is exactly what happens - the hole expands.
2) Linear dimensions of a heated piece of metal are related to
the old dimensions as follows:
L = k*l where k is the linear coefficient of heat-expansion.
L^2 = m*l^2 m is the area coefficient of ...................
L^3 = j*l^3 where j is the volume coefficient of exp.......
Note: k,m,j are dependent on material, pressure etc.
3) One of the fellows participating in the discussion posted a
seeming paradox:
if one has a disk with a hole in its centre, then
one can cut it up into a whole bunch of disks with different radii
and logically get expansion effect since their circumferences will
grow with heating, on the other hand, if one cuts the disk radially
then, seemingly, one would see the hole to contract since those slices
will expand radially as well as laterally.
The logical falacy of the second case arises from the fact that
one forgets to consider the interaction between those slices. As they
heat and expand they push against each other and move away from the
centre, still novertheless, maintaining full contact with each other
(since now they are bigger). One can perform a simple experiment to
convince himself this is so. Take a metal disk, cut it into 4 slices
(radially). Place them on a flat surface so that they form a disk, then
heat them and then let them cool. Having done the above, you will
find those slices to have moved away from the centre and no longer
touching each other.
4) Several people mention having seen some experiments performed
to show the effects of thermal expansion, I also have seen some
experiments and this is what I saw:
if one has a metal ball that barely fits into a metal ring but still
does not go through, and one hits the ring then the ball will
easily go through,
if one instead heats up the ball it will not be able to go through the
ring at all.
5) Anyway, holes do indeed expand.