The electric furnace must emit 100 kJ of heat in 10 minutes. What should be the length of a chrome wire

The electric furnace must emit 100 kJ of heat in 10 minutes. What should be the length of a chrome wire (ρ = 1.1 ∙ 10-6 Ohm ∙ m) with a cross section of 5 ∙ 10-7 m2, if the furnace is intended for a 30 V power grid?

Given: Q (the amount of heat that an electric furnace should emit) = 100 kJ (100 * 10 ^ 3 J); t (duration of work) = 10 min (600 s); S (wire section) = 5 * 10 ^ -7 m2; U (operating voltage) = 30 V.

Constants: ρ (specific electrical resistance of nichrome) = 1.1 * 10 ^ -6 Ohm * m.

We express the required length of nichrome wire from the formula: Q = U2 * t / R = U ^ 2 * t / (ρ * l / S) = U ^ 2 * t * S / (ρ * l), whence l = U ^ 2 * t * S / (Q * ρ).

Calculation: l = 30 ^ 2 * 600 * 5 * 10 ^ -7 / (100 * 10 ^ 3 * 1.1 * 10 ^ -6) = 2.45 m.