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Answer :
To find out how much energy it takes to melt a piece of aluminum foil that is already at its melting point, we need to use the concept of latent heat of fusion.
The latent heat of fusion is the amount of energy required to change a substance from a solid to a liquid at its melting point, without changing its temperature. For aluminum, this value is provided as [tex]\( L_f = 37.6 \times 10^4 \, \text{J/kg} \)[/tex].
Here's how we can calculate the energy needed:
1. Identify the mass of the aluminum piece:
- The mass of the aluminum foil is [tex]\( 0.058 \, \text{kg} \)[/tex].
2. Use the formula for energy based on latent heat of fusion:
- The formula to calculate the energy ([tex]\( Q \)[/tex]) required is:
[tex]\[
Q = \text{mass} \times \text{latent heat of fusion}
\][/tex]
- Substitute the given values into the formula:
[tex]\[
Q = 0.058 \, \text{kg} \times 37.6 \times 10^4 \, \text{J/kg}
\][/tex]
3. Calculate the energy required:
- [tex]\( Q = 0.058 \times 376000 = 21808 \, \text{Joules} \)[/tex]
So, the energy required to melt the 0.058 kg of aluminum is approximately 21,808 Joules. This result is rounded to the nearest whole number.
The latent heat of fusion is the amount of energy required to change a substance from a solid to a liquid at its melting point, without changing its temperature. For aluminum, this value is provided as [tex]\( L_f = 37.6 \times 10^4 \, \text{J/kg} \)[/tex].
Here's how we can calculate the energy needed:
1. Identify the mass of the aluminum piece:
- The mass of the aluminum foil is [tex]\( 0.058 \, \text{kg} \)[/tex].
2. Use the formula for energy based on latent heat of fusion:
- The formula to calculate the energy ([tex]\( Q \)[/tex]) required is:
[tex]\[
Q = \text{mass} \times \text{latent heat of fusion}
\][/tex]
- Substitute the given values into the formula:
[tex]\[
Q = 0.058 \, \text{kg} \times 37.6 \times 10^4 \, \text{J/kg}
\][/tex]
3. Calculate the energy required:
- [tex]\( Q = 0.058 \times 376000 = 21808 \, \text{Joules} \)[/tex]
So, the energy required to melt the 0.058 kg of aluminum is approximately 21,808 Joules. This result is rounded to the nearest whole number.
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