They forgot to turn off the 500 W electric kettle. How long does it take for all the water in the kettle to boil off?

They forgot to turn off the 500 W electric kettle. How long does it take for all the water in the kettle to boil off? Teapot capacity 2L, efficiency -50%, initial water temperature 18 ° C.

N = 500 W.

V = 2 l = 2 * 10 ^ -3 m ^ 3.

ρ = 1000 kg / m ^ 3.

Efficiency = 50%.

t1 = 18 ° C.

t2 = 100 ° C.

C = 4200 J / kg.

λ = 2.3 * 10 ^ 6 J / kg.

T – ?

Let us write down the definitions for the efficiency of the kettle: efficiency = Qw * 100% / Qe, where Qw is the amount of heat that goes to evaporate water, Qe is the amount of heat that is released in the tile.

Qw = C * m * (t2 – t1) + λ * m = m * (C * (t2 – t1) + λ).

We express the mass of water m by the formula: m = ρ * V.

Qw = ρ * V * (C * (t2 – t1) + λ).

Qe = N * T, where T is the time of passage of the current, N is the power of the tile.

Efficiency = ρ * V * (C * (t2 – t1) + λ) * 100% / N * T.

T = ρ * V * (C * (t2 – t1) + λ) * 100% / N * efficiency.

T = 1000 kg / m ^ 3 * 2 * 10 ^ -3 m ^ 3 * (4200 J / kg * (100 ° C – 18 ° C) + 2.3 * 10 ^ 6 J / kg) * 100% / 500 W * 50% = 21155 s.

Answer: the water will boil away after a time T = 21155 s.