# A brass block of cooling to -50 degrees was thrown into water weighing 100 grams at a temperature of 25

A brass block of cooling to -50 degrees was thrown into water weighing 100 grams at a temperature of 25 degrees. What is the minimum weight a bar should have for the water to freeze?

mw = 100 g = 0.1 kg.

Cw = 4200 J / kg * ° C.

q = 3.4 * 105 J / kg.

t1 = 25 ° C.

t2 = 0 ° C.

t3 = – 50 ° C.

Cl = 400 J / kg * ° C.

ml -?

In order for the water to freeze, it must first be cooled from t1 to the crystallization temperature t2, and then at this temperature it must be turned into a solid state.

The amount of heat energy Q that will be released during this process can be found by the formula: Q = Cw * mw * (t1 – t2) + q * mw.

The required amount of heat Q, to obtain ice from water, will be given by a brass part when it cools from temperature t3 to temperature t2.

Q = Cl * ml * (t2 – t3).

Cw * mw * (t2 – t1) + q * mw = Cl * ml * (t2 – t3).

The formula for determining the mass of a brass bar will take the form: ml = (Cw * mw * (t2 – t1) + q * mw) / Cl * (t2 – t3).

ml = (4200 J / kg * ° C * 0.1 kg * (25 ° C – 0 ° C) + 3.4 * 105 J / kg * 0.1 kg) / 400 J / kg * ° C * ( 0 ° C – (- 50 ° C)) = 2.225 kg.

Answer: a brass bar should have a mass of ml = 2.225 kg.

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