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GarageTinker

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This is an edited re-posting. I am looking for verification on a formula. As part of a personal design project (not for school or homework) I’m designing coils of magnet wire (i.e. coils in a generator) and I have all of the computational resources I need, with the exception of a formula to calculate the conversion of a power flow in watts to a temperature (°C or °F). I’ve been doing a good bit of searching and researching on the web and I’ve found a formula that I would like feedback on.

Now, to utilize a very useful example I found on the web; let’s say that silly me is goofing around with a 15 foot piece of 8 gauge (AWG) copper wire, which has .01 ohms of resistance and that the wire is connected directly to the positive terminal of a 12V automotive battery (no fuse, silly me) and I clumsily allow the other end to contact the negative terminal of the same battery. Dummy me is now holding a wire with 1200 amps running through it. (ouch)

I = E/R

I = 12/0.01

I = 1200 amps

I take this current and plug it into the formula P=I^2*R (or more simply E*I=P) and we get:

P = I2*R

P = (1200*1200)*0.01

P = 14,400 Watts

Or

E*I=P

12V * 1200A = 14,400W

This shows that the wire would dissipate 14,400 watts of heat which would melt the wire's insulation and more than likely ignite everything that comes into contact with the wire (fuel lines, other wires, carpet, plastic, insulation, my skin…).

I can figure out all the same information on the wire coils I'm dealing with and making for my project; however, because the manufacturers all primarily site the thermal limits of their wire insulation in terms of °C or °F etc., that's where I need to be able to figure the conversion from the above example's 14,400 Watts to °C or °F.

On a very educational site called Aus-e-tute at http://www.ausetute.com.au/. They list a specific heat formula for calculating the gain or loss of heat energy in a substance. The formula is based as: The amount of heat energy (q) in Joules gained or lost by a substance is equal to the mass of the substance (m) in grams multiplied by its specific heat capacity (Cg) multiplied by the change in temperature (final temperature - initial temperature) and is stated as: q = m x Cg x (Tf - Ti).

Now, knowing that 1 watt = 1 Joule/second; and using the conversion of 1 lb. = 453.59g, 15 feet of 8 AWG copper wire is 338.83 grams; the specific heat capacity (Cg) for copper is listed (on average) as being 0.385 and let's say the wire was laying in the shade during one of our balmy Florida summer days and it’s starting temperature (Ti) is a cool 30°C (86°F) and finally, we know from my silliness above that the wire has 14,400 watts running through it. So, from the basic laws of mathematics, I believe I can restate the formula as:

q / [(m x Cg) + Ti] = Tf

which, when the numbers are plugged in would give me:

14,400 (J/s) / {[338.83173g * 0.385 (Copper’s Cg)] + 30(°C)} = 89.75(°C) or 193.55(°F)

Preliminary calculations seem to work out well for my needs, but I would like opinions on my restatement of the formula. Basically, what I need to know is, will this calculation actually work as I think it will; even if it only gets me an accuracy of +/- a couple of °F; or am I only wishfully hallucinating.