The electric heater allows you to heat 100 kg of water from 10 ° C to 35 ° C in 18 minutes, determine the power of the heater

The electric heater allows you to heat 100 kg of water from 10 ° C to 35 ° C in 18 minutes, determine the power of the heater and the current consumed by it, if it is connected to a 220 V network.

m = 100 kg.

t1 = 10 ° C.

t2 = 35 ° C.

T = 18 min = 1080 s.

C = 4200 J / kg * ° С.

U = 220 V.

N -?

I -?

Let us find the amount of heat Q, which goes for heating water, according to the formula: Q = C * m * (t2 – t1), where C is the specific heat of water, m is the mass of heated water, t2, t1 are the final and initial water temperatures.

This amount of heat Q is emitted by the heater, therefore Q = N * T, where N is the power of the heater, T is the operating time of the heater.

C * m * (t2 – t1) = N * T.

N = C * m * (t2 – t1) / T.

N = 4200 J / kg * ° C * 100 kg * (35 ° C – 10 ° C) / 1080 s = 9722 W.

The current power N is determined by the formula: N = I * U, where I is the current in the heaters, U is the current voltage.

I = N / U.

I = 9722 W / 220 V = 44.2 A.

Answer: N = 9722 W, I = 44.2 A.