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Comment by Liftyee | Hacker News Reader

This is a very well written comment overall, but the energy loss in the wire is even worse than stated!

By modelling the wire as an (ideal) resistor and applying Ohm's law, you can get P = I^2*R. the power lost in the wire is actually proportional to the square of current through it!

Therefore, if you double the current, the heat quadruples instead of doubling! You actually have to use four times the copper (to decrease resistance by 4x and get heat under control), or the wasted energy quadruples too.

Crucially, voltage is not in the equation, so high voltages - tens or hundreds of kilovolts - are used for long distance power transmission to maximise efficiency (and other impedance-related reasons).

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I was also surprised to read that heat is proportional to the current. In addition, increasing the temperature also increases the resistance in the conductor (Cu). It's around 0.4% per 1C for Cu, around 20% more heat at 70C.

Not sure about US, yet some high current lanes (thinks of threephase ~400V x 36A; IEC 60502-1) in the households are actually made of Al, not Cu. They tend to be underground though, the wires in the walls are still Cu.

Al wire is used a lot more than most people think. Here's the big differences between Al and Cu wire.

Cu is more conductive than Al so an Al wire has to have a cross section area about 1.56 times that of a Cu with the same current capacity.

But Cu is also denser than Al so the Al wire is only about 0.47 times the weight of the Cu wire.

Al is is much cheaper than Cu so the Al wire is only about 13% the cost of the Cu wire.

Al wire is prone to oxidation and thus needs an antioxidant paste applied at connection points.

Hasn't anyone tried using silver wires?

Silver wire is used for some things, but it is a lot more expensive than copper which rules it out for most applications.

Here is a table of the conductivity (in units of 10^7 S/m), the density, and the cost of copper (Cu), aluminum (Al), silver (Ag), and gold (Au).

               Cu    Al      Ag       Au
  Conductivity 5.96  3.5     6.3      4.1
  g/cm^3       8.96  2.6    10.5     19.3
  $/kg         9.03  1.2  1030    92100

If we had a copper wire with a specified capacity in amps, here is what aluminum, silver, and gold wires of the same length and capacity would weigh and cost as a percentage of the weight and cost of the copper wire, and what their diameter would be as a percentage of the diameter of the copper wire.

      Weight  Cost  Diameter
  Al    49       7    139
  Ag   110   12646     97
  Au   310 3190000    121

Suppose Ag was as cheap as, or even cheaper than Al, would it be more useful?

Sure, we could alloy and/or plate it. You have a source on Ag cheaper than Al you'd like to disclose to the class?

Silver and gold could be a lot more useful to society if they weren't so expensive. Plenty of asteroids out there to mine.

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