How much energy is required to melt 2 kg of gold? Use the table below and this equation: [tex]Q=m L_{\text {fusion }}[/tex]
| Substance | Latent Heat Fusion (melting) (kJ/kg) | Melting Point (${ }^{\circ} C$ ) | Latent Heat Vaporization (boiling) (kJ/kg) | Boiling Point (${ }^{\circ} C$ ) |
| --------- | ------------------------------------ | --------------------------- | --------------------------------------- | -------------------------- |
| Aluminum | 400 | 660 | 1100 | 2450 |
| Copper | 207 | 1083 | 4730 | 2556 |
| Gold | 62.8 | 1063 | 1720 | 2808 |
| Hellum | 5.2 | -270 | 21 | -269 |
| Lead | 24.5 | 327 | 871 | 1751 |
| Mercury | 11.4 | -39 | 296 | 357 |
| Water | 335 | 0 | 2255 | 100 |
A. 3440 kJ
B. 125.6 kJ
C. 1720 kJ
D. 10.4 kJ
Answer (2)
We are given the equation Q = m L fusion .
Substitute the given values: m = 2 kg and L fusion = 62.8 kJ/kg .
Calculate the energy required: Q = 2 × 62.8 = 125.6 kJ .
The energy required to melt 2 kg of gold is 125.6 kJ .
Explanation
Understanding the Problem We are given the formula Q = m L fusion , where Q is the energy required to melt a substance, m is the mass of the substance, and L fusion is the latent heat of fusion. We are given that the mass of gold is m = 2 kg and the latent heat of fusion for gold is L fusion = 62.8 kJ/kg . We need to find the energy Q required to melt the gold.
Substituting Values Substitute the given values into the formula: Q = m L fusion = ( 2 kg ) ( 62.8 kJ/kg )
Calculating the Energy Calculate the value of Q :
Q = 2 × 62.8 = 125.6 kJ Therefore, the energy required to melt 2 kg of gold is 125.6 kJ.
Examples
Melting is a phase transition we often encounter in everyday life. For example, if you're a jeweler melting gold to create a custom piece, you need to know how much energy your furnace needs to supply. Knowing the latent heat of fusion and the mass of gold allows you to calculate the energy required for the phase change from solid to liquid, ensuring you have enough power to complete the melting process efficiently. This principle applies to many other materials and processes, from cooking to industrial manufacturing.
The energy required to melt 2 kg of gold is 125.6 kJ, calculated using the formula Q = m L_{fusion}. By substituting the given values for mass and latent heat of fusion, we find the correct energy. Therefore, the answer is 125.6 kJ.
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