- #1
DaTario
- 1,059
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Hi all,
I was giving a class on dilatation and I have proposed to the students a problem where two pieces of wire of two different materialswere to be glued to form a 2 meter wire.
The coeficient of linear dilatation of these two substances are alpha1 = 0.0004 and alpha2 = -0.0002, i.e., a negative linear coeficient. This means that the susbtance 2 contract when a heat source is connected to it.
The question here is to determine the length of these two pieces that sum up 2 meters.
Of course the problem has solution and the formalism yields two values L1 and L2 such that L1 + L2 = 2, as was expected. However,since the behavior of this couple is to compensate dilatation with contraction, so that the length of the junction is always 2 meters, there must be something wrong, since other combinations of values would also fit.
Consider that the formalism has yielded L1 = 0,8 and L2 = 1,2. It is OK. But now let´s transfer some heat to this junction so that L1 (the one that increases in dimension) is now 0,9 and the L2 (the one which contracts) is now 1,1. What is wrong? Wasn´t the formalism to show this non uniqueness?
Thank you
DaTario
I was giving a class on dilatation and I have proposed to the students a problem where two pieces of wire of two different materialswere to be glued to form a 2 meter wire.
The coeficient of linear dilatation of these two substances are alpha1 = 0.0004 and alpha2 = -0.0002, i.e., a negative linear coeficient. This means that the susbtance 2 contract when a heat source is connected to it.
The question here is to determine the length of these two pieces that sum up 2 meters.
Of course the problem has solution and the formalism yields two values L1 and L2 such that L1 + L2 = 2, as was expected. However,since the behavior of this couple is to compensate dilatation with contraction, so that the length of the junction is always 2 meters, there must be something wrong, since other combinations of values would also fit.
Consider that the formalism has yielded L1 = 0,8 and L2 = 1,2. It is OK. But now let´s transfer some heat to this junction so that L1 (the one that increases in dimension) is now 0,9 and the L2 (the one which contracts) is now 1,1. What is wrong? Wasn´t the formalism to show this non uniqueness?
Thank you
DaTario
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