Actually I´d say that the dimension is K^-1. https://en.wikipedia.org/wiki/Elect...stivity_and_conductivity_of_various_materials
Power Line Droop.
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Ah, I see. Of course, I missed that part. So not knowing how hot the wire gets we can't say how much it may stretch. Is that at 1 G gravity? Does the length of the run and size of the wire matter (weight of the wire)?
The thermal expansion coefficient is not affected by gravity and is uniform in all directions. It is intrinsic and thus does not depend on scale.
What I'm not sure about is the elasticity. The degree of elongation due to a constant (and one-dimensional) tension might also change with temperature.
[update] I did a bit of research and this appears to be the predominant reason for cable elongation, not thermal expansion, but an increased stretchiness that is reversible with temperature.
What I'm not sure about is the elasticity. The degree of elongation due to a constant (and one-dimensional) tension might also change with temperature.
[update] I did a bit of research and this appears to be the predominant reason for cable elongation, not thermal expansion, but an increased stretchiness that is reversible with temperature.
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Interesting.
Yeah, a copper wire expands only 16.6ppm/°C, so a 100°C temperature change would change the length by <0.2%, or <0.2m over a 100m span. I'm not sure you could hardly see that.
However the Young's modulus of elasticity decreases by ~10% over that temperature change, meaning it will stretch farther for a given strain.
However the Young's modulus of elasticity decreases by ~10% over that temperature change, meaning it will stretch farther for a given strain.
Using a real simple model you can see that it probably can be readily seen. Imagine a wire 100 m wire that is perfectly straight. Now take a 100.2 m wire between those same points but that is pulled perpendicular at the midpoint so that you have two straight lines forming a triangle (with the original straight wire). The midpoint is pulled more than three feet away from the original straight line.
The displacement is the height of a right triangle that has a base of 50 m and a hypotenuse of 50.1 m. It works out to about 3.2 m.
It's basically the same phenomenon that makes it so that if you wrapped a wire completely around a (perfectly spherical) Earth then by adding just 10 m to this 40,000,000 m long wire you would lift the wire off the ground by more than 1.5 m everywhere along the entire circumference of the Earth.
There are some alloys that exhibit an extreme example of this.
Good point, although the real-world difference would be from one sagging curve (a catenary, aka funicular, aka hyperbolic cosine) to another sagging catenary, so it might be harder to detect.
I've never worked with the elastic modulus, and I have no idea of the tension in a hanging transmission wire, so I didn't feel comfortable working out a more exact value for the the expansion due to stretching. Now I'm curious.
There's a very good treatment of the physics here.
Love that! I guess it's still awaiting a practical application. Here's another interesting heat engine:
