The heat of fusion for silver at 960.8 °C is 88.3 kJ/kg and the specific heat of silver is 0.235 kJ/kg °C. What is the energy needed to melt 100 grams of silver starting at 0 °C?

Question

Quizplus · Accepted Answer

The energy needed to melt 100 grams of silver starting at 0 °C can be calculated in two steps: first, heating the silver from 0 °C to its melting point (960.8 °C), and then melting it. The energy required to heat the silver is calculated using the specific heat capacity formula: $q = mc\Delta T$, where $m = 0.1$ kg (since 100 grams = 0.1 kg), $c = 0.235$ kJ/kg °C, and $\Delta T = 960.8$ °C. This gives $q = 0.1 \times 0.235 \times 960.8 = 22.6$ kJ. The energy required to melt the silver is calculated using the heat of fusion: $q = m \times \text{heat of fusion}$, which gives $q = 0.1 \times 88.3 = 8.83$ kJ. Adding these two energies together gives $22.6 + 8.83 = 31.43$ kJ, which rounds to $31.4$ kJ.

The Heat of Fusion for Silver at 960