To determine how much heat is needed to melt 15.0 kg of mercury at its melting point, we can use the latent heat of fusion for mercury. The latent heat of fusion is the amount of heat required to change a unit mass of a substance from solid to liquid without changing its temperature. According to the table, the latent heat of fusion for mercury is [tex]\(0.12 \times 10^5 \, J/kg\)[/tex].
Steps to solve the problem:
1. Identify the latent heat of fusion for mercury: [tex]\(0.12 \times 10^5 \, J/kg\)[/tex].
2. Identify the mass of mercury that needs to be melted: [tex]\(15.0 \, kg\)[/tex].
3. Multiply the latent heat of fusion by the mass to find the total heat needed.
Calculation:
[tex]\[ \text{Heat needed} = \text{Latent heat of fusion} \times \text{Mass} \][/tex]
[tex]\[ \text{Heat needed} = (0.12 \times 10^5 \, J/kg) \times 15.0 \, kg \][/tex]
Performing the multiplication:
[tex]\[ 0.12 \times 10^5 \, J/kg \times 15.0 \, kg = 180000.0 \, J \][/tex]
The calculated heat needed to melt 15.0 kg of mercury at its melting point is [tex]\(180000.0 \, J\)[/tex].
Therefore, the correct answer is:
[tex]\[ 1.80 \times 10^5 \, J \][/tex]
