What mass of water must be poured into an iron boiler weighing 4 kg so that 4380 kJ of heat is transferred

What mass of water must be poured into an iron boiler weighing 4 kg so that 4380 kJ of heat is transferred to the boiler with water to change the temperature from 15 ° to 100 ° C?

mk = 4 kg.

Cg = 460 J / kg * ° C.

t1 = 15 ° C.

t2 = 100 ° C.

Q = 4380 kJ = 4380 * 103 J.

Cw = 4200 J / kg * ° C.

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The amount of heat energy Q, which is communicated to the iron pot with water, is used to heat the pot and the water in it.

The amount of heat is expressed by the formula: Q = Czh * mk * (t2 – t1) + Cw * mw * (t2 – t1) = (Czh * mk + Cw * mw) * (t2 – t1).

Czh * mk + Cw * mw = Q / (t2 – t1).

Cw * mw = Q / (t2 – t1) – Czh * mk.

We express the mass of water by the formula: mw = Q / Cw * (t2 – t1) – Czh * mk / Cw.

mw = 4380 * 103 J / 4200 J / kg * ° C * (100 ° C – 15 ° C) – 460 J / kg * ° C * 4 kg / 4200 J / kg * ° C = 11.8 kg.

Answer: it is necessary to pour water mw = 11.8 kg into an iron pot.