What transformations of energy occur when water is boiled in an electric kettle? How long must the wire

What transformations of energy occur when water is boiled in an electric kettle? How long must the wire of the heating element be for the kettle to boil in 10 minutes, if it is known that it boils 15 minutes after plugging in, when the heating element is wound from the same wire 6 meters long?

With the passage of current in a conductor, electrical energy is converted into heat.

Thermal energy goes first to increase the internal energy of water, and then to transform water from a liquid to a gaseous state.

t1 = 10 min = 600 s.

t2 = 15 min = 900 s.

L2 = 6 m.

S1 = S2.

ρ1 = ρ2.

Q1 = Q2.

L1 -?

The amount of thermal energy Q that is released in the electric kettle is expressed by the formula of the Joule-Lenz law: Q = U ^ 2 * t / R, where U is the voltage to which the kettle is connected, t is the operating time of the kettle, R is the resistance of the kettle spiral.

Q1 = U ^ 2 * t1 / R1.

Q2 = U ^ 2 * t2 / R2.

We express the resistance of the teapot spiral R by the formula: R = ρ * L / S.

R1 = ρ1 * L1 / S1.

R2 = ρ2 * L2 / S2.

Q1 = U ^ 2 * t1 * S1 / ρ1 * L1.

Q2 = U ^ 2 * t2 * S2 / ρ2 * L2.

L2 = U ^ 2 * t2 * S2 / ρ2 * Q2 = U ^ 2 * t2 * S2 * ρ1 * L1 / ρ2 * U ^ 2 * t1 * S1 = t2 * L1 / t1.

L2 = 900 s * 6 m / 600 s = 9 m.

Answer: the length of the heating element must be L2 = 9 m.