How to calculate the length of the conductor for heating?

Question

Physics

There is an ordinary twisted pair copper cable.
And there is a temperature to which heating is needed, for example 30 degrees.
There is a 16 volt 4 amp power supply.
What formulas can be used to calculate the length of the wire for such conditions?

Answer 1

there is a temperature to which heating is needed, for example 30 degrees

Let's imagine several options for the environment:
1) The ambient temperature is 30 degrees. Problem solved. No heating required, no power supply required, any wire can be used.
2) The ambient temperature is above 30 degrees. The problem does not have a solution using any wire, because cooling is required.
3) Ambient temperature 20 degrees (room). To heat up to 30 degrees you need a machine with water, which has an initial temperature of 10 degrees. It is quite easy to heat up, with a fairly wide range of wire lengths, but it will take different times to heat up - after all, you can heat up in an hour, or you can in a day.
4) A room of 10 square meters and a height of 3 meters, the air temperature is 20 degrees, you need to heat the whole room to 30 degrees. What material and thickness are the walls? Does the window blow cold air? And what is the temperature outside? etc., well, you get the idea. With very good thermal insulation, you can heat up in a few hours, and with bad insulation, you can never heat up with any cable, because the power is limited by the power source - 16 * 4 = 64 watts.
5) The heater is lowered into the sea. Never heat up to 30 degrees.
In summary: the task consists of two parts :
First, the thermodynamic boundary value problem. As a rule, requires complex or very complex calculations, is typically solved by numerical methods (FEM, etc.) and as an answer you can get what heater power is required for given conditions. Let's say we got P=32 (W).
Secondly, the elementary calculation of the heater, based on the required power:
I = P / U = 32/16 = 2 (A)
R = U / I = 16/2 = 8 (Ohm)
Measure the actual resistivity of one meter of your wire. Let's say you get 1 ohm per meter, then you need 8 meters to get 8 ohms. If you are 100% sure that the wire is pure copper, then you can measure the diameter D of the copper core with a caliper, calculate the cross-sectional area S \u003d D * 3.1415926, look in the reference book for the resistivity of copper and calculate for a given thickness.

Answer 2

None, since there is not enough data on the environmental conditions in which you are going to operate the "heater". Heating up to 30 degrees in conditions of good thermal insulation and heating up to the same 30 degrees in a snowdrift are completely different things. There is also no data on the cross section of the wire.
Well, using copper as a heater is a very sad decision. Copper has excellent electrical conductivity, so to get at least some heat, you will need a lot of wires . So it's much easier to use specially designed materials for this than trying to heat the copper.