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Question

Determine the mass of an iron cube if 7.24 x 10⁵J of energy is needed to make it melt at its melting point. The latent heat of fusion for iron is 2.76 x 10⁵.

Thanks.

Answer 1

My research shows the latent heat of fusion for iron as L= 30 kilocalories per kilogram or 30 kcal/kg with specific heat of iron as 0.11 kcal/kg • °C.

30000 calories times 4.184 Joules per calorie gives L in Joules as 125520 Joules (as opposed to 276000 Joules given in the problem statement).

As a demonstration, take a cube of iron from 21° C to its melting point (1535° C)  and then to a complete liquid state.

If the heat Q needed is 12.421328 kilocalories, one would guide on the formula Q = m(cΔt + L). 

Place values to obtain 12.421328 kcal = m[(0.11 kcal/kg•°C) times (1535 − 21)° C + 30 kcal/kg].

Simplify this last to 12.421328 kcal = m(196.54 kcal/kg) or mass m = 0.0632 kilograms or 63.2 grams.