Nichrome wire paradox

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The statement

The reason why nichrome wire heat up is usually explained by the fact that it has high resistance.

is problematic because it contains a true statement but is misleading. A better version of this may read

"One reason that Nichrome is suitable for heating elements is that it's high resistivity reduces the amount of material required to manufacture a resistor of given resistance and power rating".

This tends to get shortened into what is often stated.

For a given electrical heating task the applied voltage and required power between them define the required resistance.
ie R = V^2/P

Notionally the resistance could be provided by a wide range of materials. eg Wire made from iron, copper, gold, silver, nichrome, ... . Or from Yak's butter, or carbon resistive ink or much else.
The unsuitability of some of these materials is obvious (Yak's butter, gold, ...) but others are less obviously unsuitable. As further discussed below, copper wire is seldom the best choice because it tends to melt, has a low resistivity so a large amount (relatively) is required, it changes resistance with temperature, and it oxidises quite rapidly in air. Nichrome is relatively better in all these areas.

The main reasons to use Nichrome are

• 1. It has a relatively stable resistance with temperature variation.
     Temperature coefficient of resistance per degree Celsius ~=
     Copper ....... 0.4%
     Iron .............. 0.6%
     Nichrome .. 0.015%
• 2. It tends not to oxidise rapidly at high temperatures.
• 3. It has a highish melting point.
     Nichrome ~= 1400 degrees Celsius. Copper ~= 1000 degree C. Iron ~= 1500 C.
• 4. It's high resistivity means that you can produce resistors of required resistance and power ratings with RELATIVELY small amounts of wire.
     Copper ~ 1.7 E-8 Ohm meter
     Iron 9.7 Ohm-metre
     Nichrome 100 Ohm-metre

Copper is poor in all these areas.
When used as a heating element exposed to air it tends to change resistance substantially as it heats, oxidise rapidly, melt and require long and thin wire for most applications.

Iron is not much better than copper.

For eg a 1 kW heating element operating at 100 VAC the required resistance is R = P/V = 10 Ohms.
The required element is made thick enough to not melt (required thickness depends whether air would or in contact with a thermal sink) and then long enough to produce the required resistance.

Table of resistivities here

Table of melting points here

Table of temperature coefficients of resistance here

Nichrome - from Nichrome - Wikipedia

"Almost any conductive wire can be used for heating, but most metals conduct electricity with great efficiency, requiring them to be formed into very thin and delicate wires to create enough resistance to generate heat.

When heated in air, most metals then oxidize quickly, become brittle and break. Nichrome wire, when heated to red-hot temperatures, develops an outer layer of chromium oxide, which is thermodynamically stable in air, is mostly impervious to oxygen, and protects the heating element from further oxidation.

Nichrome alloys are known for their high mechanical strength and their high creep strength. The properties of nichrome vary depending on its alloy.

Uses: Because of its low cost of manufacture, strength, ductility, resistance to oxidation, stability at high temperatures, and resistance to the flow of electrons, nichrome is widely used in electric heating elements ... "