Or perhaps you could ponder the wisdom of those here who have before used hot wire to cut plastic foam. Perhaps such a device could also be used for cutting ice cream?

There's is some subtlety involved in the design of heating elements.

Consider the following koan, to help prepare your mind:

The wires in a toaster glow orange-hot, and these wires share the same current as the wires in the wall connected to the toaster. Yet the wires in the wall, do not glow orange-hot. The wires in the wall stay cool. Why is this so?

Well, the answer is that the amount of power dissipated by a resistor is I^{2}*R, and if you have a bunch of resistors all in series, the largest R dissipates the most power.

Ah... but what if you make one of the Rs infinite (same as an "open" circuit)? What happens then? Then the amount of power dissipated by all the resistors becomes zero, because the current is zero.

So you have to make the R of your heating element large, larger than the other resistances in the circuit, but not too large... Not too small either, or your R then it might just burn itself up.

The resistance of a length of wire...

is proportional to its length, inversely proportional to the cross-section area, and proportional to this other number called resitivity. The equation looks like this:

R = ρ*(l/A)

Nichrome has larger resistivity ρ than copper.

Divide both sides by unit l, and you get resistance per unit length. Just like you'd expect, thin wire (small A) has large resistance per unit length.

R/l = ρ/A

So that's, roughly, how you calculate the resistance of a given length of wire. Often there is also a correction for temperature too. The resistance of metals usually increases somewhat with increasing temperature.

These equations, along with Ohm's Law and Kirchhoff's rules, will indeed be helpful, if you want to take a wire and make it hot, and keep everything else cool at the same time.

Without these equations, you'll need a lot of trial and error.

Re-design's suggestion is the closest thing to recipe among these answers, since he gives you some numbers that sound believable, (12V) ^{2}/(20 Ω )= 7.2 W, Plus, following this recipe, you don't have to go to the trouble of designing a resistor, You can just buy one. In fact if you're totally new to the subject of Ohm's law and circuits, and math, etc, then RD's answer might be a good place to start.

Just a thought: a sharp edge is all you need to cut through the ice cream, the problem is that the rest of the scoop tends to stick to the ice cream. Are you only planning to heat the cutting edge, or the whole scoop?

I'm gonna just throw out my first thoughts. High possibility of electrocution and the simple inconvenience of burning your icecream (a wire hot enough to cut thru the icecream would likely be hot enough at the surface to cook the milk products unless controlled very well to keep the temp low enough not to burn at contact yet high enough to effectively cut the icecream) are two reasons I'm not sure I'd attempt this one. But mainly the first.

This sounds like something that might work better on a larger scale than a handheld scoop, but in any case you might look into nichrome wire instead of copper. Nichrome makes a better heating element for most applications than copper.

You don't really need to warm wire, unless the ice cream is particularly hard? If the wire isn't thin, you'll need a heavy power supply to get it warm...

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Consider the following koan, to help prepare your mind:

Well, the answer is that the amount of power dissipated by a resistor is I

^{2}*R, and if you have a bunch of resistors all in series, the largest R dissipates the most power.Ah... but what if you make one of the Rs infinite (same as an "open" circuit)? What happens then? Then the amount of power dissipated by all the resistors becomes zero, because the current is zero.

So you have to make the R of your heating element large, larger than the other resistances in the circuit, but not too large... Not too small either, or your R then it might just burn itself up.

The resistance of a length of wire...is proportional to its length, inversely proportional to the cross-section area, and proportional to this other number called resitivity. The equation looks like this:

Nichrome has larger resistivity ρ than copper.

Divide both sides by unit l, and you get resistance per unit length. Just like you'd expect, thin wire (small A) has large resistance per unit length.

So that's, roughly, how you calculate the resistance of a given length of wire. Often there is also a correction for temperature too. The resistance of metals usually increases somewhat with increasing temperature.

These equations, along with Ohm's Law and Kirchhoff's rules, will indeed be helpful, if you want to take a wire and make it hot,

andkeep everything else cool at the same time.Without these equations, you'll need a lot of trial and error.

Re-design's suggestion is the closest thing to recipe among these answers, since he gives you some numbers that sound believable,

(12V)

^{2}/(20 Ω )= 7.2 W,Plus, following this recipe, you don't have to go to the trouble of designing a resistor, You can just buy one. In fact if you're totally new to the subject of Ohm's law and circuits, and math, etc, then RD's answer might be a good place to start.

If the wire isn't thin, you'll need a heavy power supply to get it warm...

L

Then start very low and see what temperature you get. Don't go over 12 volts. Both the resistor and wire will get hot so be careful.