The iron billet, cooling from 800 to 0 degrees, melted ice weighing 3 kg. taken at a temperature of 0 degrees.

The iron billet, cooling from 800 to 0 degrees, melted ice weighing 3 kg. taken at a temperature of 0 degrees. What is the mass of the workpiece if all the energy released during its cooling was used to melt the ice?

Q1 = Q2 (we assume that the heat from the iron workpiece goes to melting the ice, and the resulting water does not heat up).

Q1 (billet cooling) = С * m1 * (t2 – t1), where С (specific heat capacity of iron) = 460 J / (K * kg), m1 (weight of iron billet), t2 (initial temp.) = 800 ºС, t1 (end temp.) = 0 ºС.

Q2 (ice melting) = λ * m2, where λ (beats heat of fusion) = 3.4 * 10 ^ 5 J / kg), m2 (ice mass) = 3 kg.

C * m1 * (t2 – t1) = λ * m2.

m1 = λ * m2 / (C * (t2 – t1)) = 3.4 * 10 ^ 5 * 3 / (460 * 800) = 2.77 kg.