The heat of fusion for gold at 1,063 °C is 66.6 kJ/kg and the specific heat of gold is 0.128 kJ/kg °C. What is the energy needed to melt 100 grams of gold starting at 0 °C?

Question

Quizplus · Accepted Answer

To calculate the energy needed to melt 100 grams of gold starting at 0 °C, we need to consider both the energy required to raise the temperature of gold to its melting point and the heat of fusion needed to melt it. First, calculate the energy to raise the temperature to 1063 °C using the specific heat capacity: $E_1 = m \cdot c \cdot \Delta T = 0.1 \, \text{kg} \cdot 0.128 \, \text{kJ/kg °C} \cdot 1063 \, °C = 136.064 \, \text{kJ}$. Then, calculate the energy needed for the phase change using the heat of fusion: $E_2 = m \cdot \text{heat of fusion} = 0.1 \, \text{kg} \cdot 66.6 \, \text{kJ/kg} = 6.66 \, \text{kJ}$. The total energy is the sum of $E_1$ and $E_2$, but since the calculation for $E_1$ was incorrect (it should have been calculated only for the phase change, not raising the temperature), the correct approach focuses solely on the heat of fusion for melting: $E = m \cdot \text{heat of fusion} = 0.1 \, \text{kg} \cdot 66.6 \, \text{kJ/kg} = 6.66 \, \text{kJ}$. However, the initial calculation mistake led to an incorrect explanation. The correct calculation should only involve the heat of fusion since the question specifically asks for the energy needed to melt gold, implying the phase change, not the warming phase. Therefore, the correct energy needed is directly calculated from the heat of fusion: $E = 0.1 \, \text{kg} \cdot 66.6 \, \text{kJ/kg} = 6.66 \, \text{kJ}$, which does not match any of the provided options directly, indicating a mistake in the calculation or interpretation of the question. The correct approach is to recognize the error in the explanation regarding the application of specific heat for this scenario. The question's focus is on melting, thus primarily involving the heat of fusion.

The Heat of Fusion for Gold at 1,063 °C Is