The hotplate, the spiral resistance of which is 10 ohms, is connected to a 200 volt network.

The hotplate, the spiral resistance of which is 10 ohms, is connected to a 200 volt network. water weighing 1 kg, having an initial temperature of 20 degrees, is poured into an aluminum pan weighing 500 g and put on this electric stove. after what time will the water boil if we neglect the energy losses in the air?

R = 10 ohms.

U = 200 V.

mw = 1 kg.

Cw = 4200 J / kg * ° С.

Ca = 900 J / kg * ° С.

mk = 500 g = 0.5 kg.

t1 = 20 ° C.

t2 = 100 ° C.

T -?

The amount of thermal energy Q, which is released in the tile, is found according to the Joule-Lenz law: Q = U ^ 2 * T / R.

The amount of thermal energy Q, which is necessary for heating water and a saucepan, can be found by the formula: Q = Cw * mw * (t2 – t1) + Ca * mk * (t2 – t1) = (Cw * mw + Ca * mk) * ( t2 – t1).

U ^ 2 * T / R = (Cw * mb + Ca * mk) * (t ^ 2 – t1).

T = (Cv * mv + Ca * mk) * (t2 – t1) * R / U ^ 2.

T = (4200 J / kg * ° C * 1 kg + 900 J / kg * ° C * 0.5 kg) * (100 ° C – 20 ° C) * 10 Ohm / (200 V) 2 = 93 s.

Answer: water will boil in time T = 93 s.