When an electric current of 5 A passed through the coil of a heater made of nickelin wire with

When an electric current of 5 A passed through the coil of a heater made of nickelin wire with a cross-sectional area of 0.75 mm2, an amount of heat of 680800 J was released in 13 minutes. What is the length of the wire from which the coil is made?

Task data: I (electric current) = 5 A; S (cross-sectional area of the heater coil) = 0.75 mm2; t (heater operation time) = 13 min (in SI t = 780 s); Q (released heat) = 680800 J.

Constants: ρ (specific resistance of nickel at 20 ºС) = 0.4 Ohm * mm2 / m.

1) Let’s calculate the resistance of the heater coil: Q = I ^ 2 * R * t and R = Q / (I ^ 2 * t) = 680800 / (5 ^ 2 * 780) = 34.91 Ohm.

2) Determine the length of the nickel wire: R = ρ * l / S and l = R * S / ρ = 34.91 * 0.75 / 0.4 = 65.46 m.