# Finding the temperature of a wire

1. Apr 15, 2014

### kern23

Is there a formula for finding the temperature of a wire?
If I know how many volts I put on a wire, the resistance of the wire per foot, the length of the wire, and the ambient air temperature. Is that enough information to determine what the wire's temperature will be? Do I need more information to figure this out?

Any advice or a formula so I can plug in the numbers would be much appreciated.

Thanks

2. Apr 15, 2014

### Staff: Mentor

Hi Kern23. Welcome to physics forums.

There is an additional piece of information you need. This is the heat transfer coefficient between the outside surface of the wire and the ambient air. The wire surface will be at a different temperature than the air (i.e., the air away from the wire). The rate of heat loss from the wire per unit area of wire will be proportional to the difference in temperature, with the constant of proportionality being the heat transfer coefficient. If the wire is horizontal and "levitated" in the air so that it is not in contact with anything else along its length, the heat transfer coefficient to the air is controlled by natural convection heat transfer. You can look up natural convection heat transfer from a cylinder in heat transfer textbooks. It depends on several physical properties of the air, and on the diameter of the cylinder. This calculation of the heat transfer coefficient will provide closure on your analysis, and will enable you to calculate the wire temperature at steady state.

Chet

3. Apr 15, 2014

### Baluncore

Most native metal wires have a temperature coefficient of resistance that is close to linear and passes through the absolute zero kelvin origin. Resistance is therefore proportional to absolute temperature.

As an example, a lamp filament that has a resistance of 10 ohms at about room temperature 300 K, will have a resistance of 20 ohms at 600 K and 100 ohms at 3000 K.

You can estimate the absolute temperature of a non-alloyed wire by measuring the current and voltage from which you can compute resistance and absolute temperature.

Alloyed wires can have a quite interesting temperature – resistance relationship.

4. Apr 16, 2014

### Staff: Mentor

This method works if you measure both the current and voltage. If you only measure the voltage (as in the original post), you can still predict the temperature of the wire if you combine this method with the approach I recommended in my earlier post, which involves using natural convection heat transfer correlations to get the heat transfer coefficient.

Chet

5. Apr 16, 2014

### Baluncore

The problem is that the resistance will change depending on the temperature.
Measuring the resistance of the wire is alone sufficient to work out the temperature.
http://en.wikipedia.org/wiki/Temper...perature_coefficient_of_electrical_resistance
http://en.wikipedia.org/wiki/Resistivity#Resistivity_of_various_materials (includes coefficient).

6. Apr 16, 2014

### kern23

So this method would not work with a wire that is an alloy?
If not, then is the method that Chestermiller stated the only method to use?
Or is there a different approach to this if I also know the current expected to flow through the wire (which I could figure out)?

7. Apr 16, 2014

### Baluncore

What wire material did you plan to use?

8. Apr 16, 2014

### kern23

Nichrome 80 and it would have insulation on it.

9. Apr 16, 2014

### Staff: Mentor

If the wire has insulation, then it will provide thermal insulation as well (i.e., low thermal conductivity), and this needs to be taken into account when applying the method that I recommended.

Chet

10. Apr 16, 2014

### kern23

Perhaps it would help if I told you I don't need a specific temperature. I'm just wondering how much current or voltage or watts would need to be put through a wire to maintain a temperature above freezing when the air temperature is at or slightly below freezing. Much like the defroster wires work on a vehicles rear window to clear the frost or light snow.
Does that simplify things? Or is this still a complex problem with many variables to consider?

11. Apr 16, 2014

### Staff: Mentor

Is it that you were just wondering, or is there a specific system with a specific geometry that you haven't revealed yet. If there is, please describe it in detail. Otherwise, we are dealing with a moving target.

Chet

12. Apr 16, 2014

### kern23

Yes, I would like to do essential the same thing as what is on a vehicles rear window. The difference would be the length of the wire and the applied voltage. But I'm looking for it to do the same function as a window defroster.

13. Apr 16, 2014

### Staff: Mentor

OK. Give us some geometric dimensions and layout, including wire diameter, glass thickness, wire placement within glass, spacing between adjacent wires, etc.

Chet

14. Apr 16, 2014

### kern23

Ok, I will figure those details out and get back to you. Thanks

15. Apr 17, 2014

### kern23

Alright, so here are the detail I know. The length of wire I am shooting for is 10 feet. This would be attached to the surface of 1/4 inch thick clear plastic (not glass) in a horizontal pattern, this is that it would run horizontal for one foot (right) then turn vertical for one inch (down) then turn horizontal again headed back the other direction (left). There would be a total of 7 horizontal runs and 7 vertical runs (total of 7' 7") the other 2' 5" would be brought back to a 9 volt battery. The wire I was thinking about using would be Nichrome 80, 20 AWG which has a diameter of 0.032 inches, its resistance is 0.6348 ohms per foot. That is just my guess as to what wire size I need, if it turns out I need more or less resistance in the wire the size can be changed to make it work. Hopefully this added information can help out.

16. Apr 17, 2014

### Staff: Mentor

Didn't you say the wire would have an insulating coating?

17. Apr 18, 2014

### Staff: Mentor

OK. Just a few more details. What is the nature of the wire attachment to the plastic sheet? Is the sheet going to be oriented horizontally or vertically or ?? Is there usually going to be air flow over the sheet, or is it sometimes going to be in static air? Do you have any numbers on the thermal conductivity of the plastic? What is the melting point of the plastic? I assume that the heat from the wire is supposed to heat the opposite side of the sheet (where frost may be present), correct?

Chet

18. Apr 22, 2014

### kern23

The wire will be attached with glue. The plastic will be vertical. It will usually have around 20 miles per hour air flow on it. As for the information on the plastic, all I know is that it is a face shield for a snowmobile helmet, so whatever that makes it. Lastly, yes I plan to attach the wire on the side of the plastic where frost would appear.

19. Apr 22, 2014

### Staff: Mentor

OK. So there would be an area of ~ 1' x 6" of wire laid out on a snowmobile face shield. The length of the wire would be 10 ft, and the resistance would be 0.6348 ohms per foot. You would be using a 9 volt battery, so the current would be about 1.4 amps (how long will the battery charge last with this current?). The heating rate would be about 13 W, or about 0.1 W/inch. Since the spacing of the wires is 1", each square inch of heated surface receives a heating rate of 0.1 W, or, the surface heating rate is 0.1 W/in2. This is an area-average heating rate of about 50 BTU/hr ft2. Does this make sense so far?

If it is a snowmobile face shield, I'm assuming that the long direction of the heated area is vertical, and the short direction of the the heated area is horizontal. Correct? The 20 mph air flow hits the face shield head-on, correct? The face shield is not perfectly flat? It is curved around the face, correct? The air flows around the curved face shield?

Chet