For cooling, a copper piece with a temperature of 100 degrees was immersed in water weighing 420 g

For cooling, a copper piece with a temperature of 100 degrees was immersed in water weighing 420 g at a temperature of 15 degrees. Determine the mass of the part if the water has heated up to 18 degrees during the heat exchange.

In this case, heat is transferred from the copper part to the water.

According to the rule, an amount of heat was transferred from the copper part equal to:

Q1 = c1 * m1 * (t1 – t2), where t1 is 100 degrees, t2 is 18 degrees.

In this case, the water received an amount of heat equal to:

Q2 = c2 * m2 * (t2 – t3), where t2 – 18 degrees, t3 – 15 degrees.

c1 * m1 * (t1 – t2) = c2 * m2 * (t2 – t3)

m1 = c2 * m2 * (t2 – t3) / ((t1 – t2) * c1).

m1 = 4200 * 0.42 * (18 – 15) / (385 * (100 – 18)) = 167 g.

Answer: the mass of the copper part is 167 g.