Given 2 wires of the same length and section (iron and copper), connected in parallel. Which one produces more heat?

1. The power of the heater is determined by the formula:
P = Q / τ, Q – where the amount of heat, τ – heating time.
The amount of heat released:
Qzh = Pzh * τ
Qm = Pm * τ
2. Formula for determining electrical power:
Pzh = U² / Rzh
Pm = U² / Rm
(When connected in parallel, the voltage at the ends of each wire is the same)
3. Let’s write down the expression to determine the resistivity of the wire:
ρsp = R * Ssech / l, where R is the resistance of the wire, l is the length of the wire, Ssech is the cross-sectional area.
Let us express R from here:
R = ρsp * l / Ssection
Rzh = ρudzh * l / Ssec
Rm = ρudm * l / Ssec
4. Substitute all this into the expression for the amount of heat:
Qzh = Pzh * τ = U² * τ / Rzh = U² * τ * Ssec / (ρudzh * l)
Qm = U² * τ * Ssection / (ρudm * l)
5. Divide Qm / Qzh:
Qm / Qzh = (U² * τ * Ssec / (ρudm * l)) / (U² * τ * Ssec / (ρudzh * l)) = (U² * τ * Ssec * ρudzh * l) / (ρudm * l * U² * τ * Ssection) = ρudzh / ρudm
6. Substitute the numbers and find the difference:
According to the reference book, resistivity: ρudzh = 9.8 ** 10 ^ -8 Ohm * m, ρudm = 1.7 * 10 ^ -8 Ohm * m.
Qm / Qzh = ρudzh / ρudm = 9.8 ** 10 ^ -8 / 1.7 * 10 ^ -8 = 5.76 times.
Answer: 5.76 times more heat will be released on a copper conductor.