# Calculating Temperature of Resistance Wire based on Power?

#### ultrahacker01

Joined Dec 4, 2017
3
Hello, I have a question that relates to heating element project I am working on. Based on joule's law, we can derive the energy lost (load) from running electricity through a wire.
J = I^2 * R
(r = resistance in ohms, I = current in amps).

Using this fact that resistance in wire releases energy (joules) in the form of heat, I'm wondering if we know what the wire is made of, it's size and length, the resistance (per cm) and the power running through it, could I get an exact temperature rise?

#### strantor

Joined Oct 3, 2010
5,178
Hello, I have a question that relates to heating element project I am working on. Based on joule's law, we can derive the energy lost (load) from running electricity through a wire.
J = I^2 * R
(r = resistance in ohms, I = current in amps).

Using this fact that resistance in wire releases energy (joules) in the form of heat, I'm wondering if we know what the wire is made of, it's size and length, the resistance (per cm) and the power running through it, could I get an exact temperature rise?
yes, assuming there is no cooling action anywhere on the wire.
This sounds like a hot wire foam cutter application so I will use that as an example.
Say if you have 12" of nichrome wire and put a specific current thru it, you can calculate the temperature of the wire and that will be accurate across the length of wire.
But if you start to push a 1" piece of foam through it, that foam will be cooling the wire through 1" of the wire.
now your calculation will return an average temperature, the average of 11" of hotter wire and 1" of cooler wire.
The calculation will not be accurate for either the hotter wire or the cooler wire, but somewhere in the middle.
In real life this probably isn't enough deviation to matter. But if you're interested in absolute accuracy for the sake of absolute accuracy (for academic reasons or so) then, no, not accurate.

#### ultrahacker01

Joined Dec 4, 2017
3
I am trying to make a 3d printer heated that heats up in seconds rather than minutes using AC mains voltage (at my house 120v), and around 8-10 amps. I could just buy a 120v hot plate (for cooking), but I need it to be a pretty specific size, and buying ni-chrome would be fairly cheap. Is there an equation for determinging temperature based on Amperage?

#### Alec_t

Joined Sep 17, 2013
10,616
No simple equation. The energy dissipated in a given wire can be easily calculated, but the temperature can't, because of unknown heat loss through conduction at the end supports of the wire, by convection, and by radiation into surroundings of unknown thermal conductivity/capacity
Beware of powering the wire directly from the mains. The whole equipment could become fatally live unless due precautions are taken.

#### strantor

Joined Oct 3, 2010
5,178
I am trying to make a 3d printer heated that heats up in seconds rather than minutes using AC mains voltage (at my house 120v), and around 8-10 amps. I could just buy a 120v hot plate (for cooking), but I need it to be a pretty specific size, and buying ni-chrome would be fairly cheap. Is there an equation for determinging temperature based on Amperage?
my 3D printer hotbed is a PCB with criss-cross routed tracks that heat up. You can do it with nichrome wire but the PCB route would probably be easier.
you will most likely have to come up with your own formula because like in my PCB hotbed, the FR4 matierial it's made of conducts some heat. I assume your setup, PCB or otherwise, will have some body that conducts heat. It will take some time to reach a steady temp once you apply the known current.
I would get the resistance of the element, and calculate the proper voltage to apply, to get the desired current.
Then apply that current while having some temp probe on the bed, and see how long it takes to reach stead temp

#### ultrahacker01

Joined Dec 4, 2017
3
Thank you! I will be using a solid state relay controlled by the 3DP control board that turns on and off with the thermistor value. I also seem to have found a super helpful website that shows me the temperature of the ni-chrome wire they sell, based on amperage applied. http://www.jacobs-online.biz/nichrome_wire.htm . My plan was to some sort of polymer clay to make a sort of ceramic heater. You said the PCB route would be easier, how would I go about using a PCB?
my 3D printer hotbed is a PCB with criss-cross routed tracks that heat up. You can do it with nichrome wire but the PCB route would probably be easier.
you will most likely have to come up with your own formula because like in my PCB hotbed, the FR4 matierial it's made of conducts some heat. I assume your setup, PCB or otherwise, will have some body that conducts heat. It will take some time to reach a steady temp once you apply the known current.
I would get the resistance of the element, and calculate the proper voltage to apply, to get the desired current.
Then apply that current while having some temp probe on the bed, and see how long it takes to reach stead temp

#### wayneh

Joined Sep 9, 2010
16,129
Is there an equation for determinging temperature based on Amperage?
Yes, but you wouldn't like it. It has to account for heat loss by conduction, convention and radiation, to arrive at the steady-state temperature that simultaneously satisfies all the conditions. Engineers do this all the time but even they struggle to estimate all the various parameters.

#### WBahn

Joined Mar 31, 2012
24,980
yes, assuming there is no cooling action anywhere on the wire.
If there is no cooling action anywhere on the wire, then the temperature will continue to rise until the wire melts.

If it is stable at some temperature despite power being dumped into it, then you know no only that there IS cooling action going on, but you know that the amount of cooling is exactly sufficient to carry away just the amount of power being dumped into it.

#### WBahn

Joined Mar 31, 2012
24,980
Hello, I have a question that relates to heating element project I am working on. Based on joule's law, we can derive the energy lost (load) from running electricity through a wire.
J = I^2 * R
(r = resistance in ohms, I = current in amps).

Using this fact that resistance in wire releases energy (joules) in the form of heat, I'm wondering if we know what the wire is made of, it's size and length, the resistance (per cm) and the power running through it, could I get an exact temperature rise?
Not unless you can exactly model ALL of the thermal losses as a function of temperature.

#### strantor

Joined Oct 3, 2010
5,178
Thank you! I will be using a solid state relay controlled by the 3DP control board that turns on and off with the thermistor value. I also seem to have found a super helpful website that shows me the temperature of the ni-chrome wire they sell, based on amperage applied. http://www.jacobs-online.biz/nichrome_wire.htm . My plan was to some sort of polymer clay to make a sort of ceramic heater. You said the PCB route would be easier, how would I go about using a PCB?

#### strantor

Joined Oct 3, 2010
5,178
If there is no cooling action anywhere on the wire, then the temperature will continue to rise until the wire melts.

If it is stable at some temperature despite power being dumped into it, then you know no only that there IS cooling action going on, but you know that the amount of cooling is exactly sufficient to carry away just the amount of power being dumped into it.
Good nitpick. I'm pretty sure it was obvious what I was talking about though. Uneven Cooling, and Cooling above what ambient provides.

#### ebeowulf17

Joined Aug 12, 2014
2,969
In theory, since resistance varies as a function of temperature, you could measure the voltage across the element and the current through the element, calculate the resistance, and from there determine the temperature.

In practice, I'm guessing there are myriad reasons why it would be impractical to do it this way.