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

To solve this problem, we need to calculate the energy required in two stages:

1. Heating the gold from 0 °C to its melting point (1,063 °C)
2. Melting the gold at its melting point

Step 1: Heating the gold from 0 °C to its melting point (1,063 °C)

The energy required to heat an object is given by the formula:

Q = mcΔT

where: Q = heat energy (kJ) m = mass (kg) c = specific heat capacity (kJ/kg °C) ΔT = change in temperature (°C)

First, we need to convert the mass from grams to kilograms:

100 g = 0.1 kg

Then we can substitute the values into the formula:

Q = 0.1 kg * 0.128 kJ/kg °C * 1,063 °C = 13.61 kJ

Step 2: Melting the gold at its melting point

The energy required to melt a substance is given by the formula:

Q = mL

where: Q = heat energy (kJ) m = mass (kg) L = heat of fusion (kJ/kg)

Substituting the values into the formula gives:

Q = 0.1 kg * 66.6 kJ/kg = 6.66 kJ

Finally, we add the energy required for both stages to get the total energy required:

Total energy = 13.61 kJ + 6.66 kJ = 20.27 kJ

So, the energy needed to melt 100 grams of gold starting at 0 °C is 20.27 kJ.