The heat of fusion for gold at $1,063{ }^{\circ} \mathrm{C}$ is $66.6 \mathrm{~kJ} / \mathrm{kg}$ and the specific heat of gold is $0.128 \mathrm{~kJ} / \mathrm{kg}{ }^{\circ} \mathrm{C}$. What is the energy needed to melt 100 grams of gold starting at $0{ }^{\circ} \mathrm{C}$ ?

Question

Quizplus · Accepted Answer

To calculate the energy needed, first calculate the energy to heat the gold to its melting point: $Q_1 = mc\Delta T = 0.1 \, \text{kg} \times 0.128 \, \text{kJ/kg°C} \times 1063 \, \text{°C} = 13.6 \, \text{kJ}$. Then, calculate the energy to melt the gold: $Q_2 = mL_f = 0.1 \, \text{kg} \times 66.6 \, \text{kJ/kg} = 6.66 \, \text{kJ}$. Total energy $Q = Q_1 + Q_2 = 13.6 \, \text{kJ} + 6.66 \, \text{kJ} = 20.26 \, \text{kJ}$, which rounds to 20.3 kJ.

The Heat of Fusion for Gold At 1,063∘C1,063{ }^{\circ} \mathrm{C}1,063∘C Is 66.6 kJ/kg66.6 \mathrm{~kJ} / \mathrm{kg}66.6 kJ/kg

The Heat of Fusion for Gold At $1,063{ }^{\circ} \mathrm{C}$ Is $66.6 \mathrm{~kJ} / \mathrm{kg}$