Re: coefficient of expansion
- From: "PD" <TheDraperFamily@xxxxxxxxx>
- Date: 5 Mar 2007 08:35:07 -0800
On Mar 4, 8:58 pm, "Jon Slaughter" <Jon_Slaugh...@xxxxxxxxxxx> wrote:
Why when you heat a metal with a hole in it then the hole grows and not
"shrink"? Why doesn't the metal expand in all directions instead of "prefer"
a direction(how does it know which is "outer" and "inner")?
I thought I remembered doing a problem in physics class where we had to
compute the new radius of a hole in a metal after it was heated and I
thought it shrunk. this means the metal expanded in all directions. Yet I
just watched a video where they guy sticks a metal sphere through a ring by
heating up the ring.
suppose I have an annulus R = {(x,y) | 1-a < sqrt(x^2 + y^2) < 1+b}
Then when I heat R why does a decrease while b increases? My intuition is
telling me a will a should go up while b goes up because the metal will
expand in all directions and that there should be no perfered direction.
Yet clearly the experiments I have seen contradict this.
Think about it this way. Suppose the atoms on the inside of the ring
are linked by bonds, like people standing in a ring and holding hands.
What you are imagining, I suppose, is that the material on the
interior of the annulus pushes the atoms on that boundary toward the
center.
However, if they did so, the atoms would have to get closer together
to form a smaller ring -- same number of atoms on inside of the ring,
smaller circumference. This should ring a little bell of alarm. When a
material expands due to increasing temperature, the spacing between
all the atoms should *increase* not decrease.
(The exercise of having students hold hands in a ring is useful for
this, especially if you tell them that in order to heat up, they
should shake their arms vigorously. The circumference of the people
ring will naturally increase.)
I just can't understand why there is a prefered direction and how the
material knows it has an inside and outside? My logic would be something
like making a small cut in the ring so that there really is no inside or
outside yet by the same logic the "hole" should get larger instead of
smaller. In this case the cut ring is more like a bent bar and this would
imply that the bar has expanding on one side more than the other). (hard to
explain but if you cut the annulus you can then bend it into a bar and I
would expect that the bar would expand in all directions uniformly and just
because it is bent into a circle shouldn't chang that fact).
Yes, it does. Notice that if you bend the bar into a circle, now if
you make the bar fatter and in so doing push the material into the
empty middle, the inner circumference of the bar *decreases*. That
doesn't happen in a straight bar.
Here's another way to think of it. Take a straight bar and bend it
into a circle. Now take an identical bar and heat it and then bend the
heated bar into a circle. Now compare all the dimensions of the second
case with that of the first case.
PD
.
- References:
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- From: Jon Slaughter
- coefficient of expansion
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