Type the correct answer in the box. Express your answer to three significant figures. Agoldsmith melts 12.4 grams of gold to make a ring. The temperature of the gold rises from 26^circ C to 1064^circ C, and then the gold melts completely. If gold's specific heat is 0.1291joules/gram degree Celsius and its heat of fusion is 63.5 joules/gram, how much energy is gained by the gold? The gold gains a total of square joules of energy.

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Type the correct answer in the box. Express your answer to three significant figures. Agoldsmith melts 12.4 grams of gold to make a ring. The temperature of the gold rises from 26^circ C to 1064^circ C, and then the gold melts completely. If gold's specific heat is 0.1291joules/gram degree Celsius and its heat of fusion is 63.5 joules/gram, how much energy is gained by the gold? The gold gains a total of square joules of energy.

Answer 1

### The gold gains a total of 2447 joules of energy.

Answer 2

## Step 1: Calculate the energy required to raise the temperature of gold to its melting point ### Use the formula $Q = mc\Delta T$, where $m$ is the mass, $c$ is the specific heat, and $\Delta T$ is the change in temperature. \[ Q_1 = 12.4 \, \text{g} \times 0.1291 \, \frac{\text{J}}{\text{g} \cdot \degree \text{C}} \times (1064 \, \degree \text{C} - 26 \, \degree \text{C}) \] \[ Q_1 = 12.4 \times 0.1291 \times 1038 \] \[ Q_1 = 1659.6 \, \text{J} \] ## Step 2: Calculate the energy required to melt the gold ### Use the formula $Q = mL_f$, where $m$ is the mass and $L_f$ is the heat of fusion. \[ Q_2 = 12.4 \, \text{g} \times 63.5 \, \frac{\text{J}}{\text{g}} \] \[ Q_2 = 787.4 \, \text{J} \] ## Step 3: Sum the energies to find the total energy gained ### Add the energy required to raise the temperature and the energy required to melt the gold. \[ Q_{\text{total}} = Q_1 + Q_2 \] \[ Q_{\text{total}} = 1659.6 \, \text{J} + 787.4 \, \text{J} \] \[ Q_{\text{total}} = 2447 \, \text{J} \]

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