Answer :
To calculate the amount of energy needed to melt 100 kg of aluminum at its melting point, you can follow these steps:
1. Identify the Latent Heat of Fusion: This is the amount of energy required to change 1 kg of the substance from solid to liquid without changing its temperature. For aluminum, the latent heat of fusion is [tex]\(93 \, \frac{\text{kcal}}{\text{kg}}\)[/tex].
2. Determine the Mass of Aluminum: We are given that the mass of aluminum to be melted is 100 kg.
3. Calculate the Total Energy Needed: To find the total energy required to melt the aluminum, multiply the mass of the aluminum by its latent heat of fusion:
[tex]\[
\text{Energy needed} = \text{Latent Heat of Fusion} \times \text{Mass of Aluminum}
\][/tex]
Substituting the values we have:
[tex]\[
\text{Energy needed} = 93 \, \frac{\text{kcal}}{\text{kg}} \times 100 \, \text{kg} = 9300 \, \text{kcal}
\][/tex]
Therefore, the amount of energy needed to melt 100 kg of aluminum at its melting point is 9300 kcal.
1. Identify the Latent Heat of Fusion: This is the amount of energy required to change 1 kg of the substance from solid to liquid without changing its temperature. For aluminum, the latent heat of fusion is [tex]\(93 \, \frac{\text{kcal}}{\text{kg}}\)[/tex].
2. Determine the Mass of Aluminum: We are given that the mass of aluminum to be melted is 100 kg.
3. Calculate the Total Energy Needed: To find the total energy required to melt the aluminum, multiply the mass of the aluminum by its latent heat of fusion:
[tex]\[
\text{Energy needed} = \text{Latent Heat of Fusion} \times \text{Mass of Aluminum}
\][/tex]
Substituting the values we have:
[tex]\[
\text{Energy needed} = 93 \, \frac{\text{kcal}}{\text{kg}} \times 100 \, \text{kg} = 9300 \, \text{kcal}
\][/tex]
Therefore, the amount of energy needed to melt 100 kg of aluminum at its melting point is 9300 kcal.
