# Solid aluminum has a specific heat of 0.89 J/g oC, and a heat of fusion of 398 J/g. Aluminum melts at 660.4oC. How much heat is required to convert a 10.0 g sample of aluminum metal at 580.0oC to a fully-molten sample of liquid at 660.4oC?

## Solid aluminum has a specific heat of 0.89 J/g oC, and a heat of fusion of 398 J/g. Aluminum melts at 660.4oC. How much heat is required to convert a 10.0 g sample of aluminum metal at 580.0oC to a fully-molten sample of liquid at 660.4oC?

Jun 2, 2016

I found: $4695.6 J$

#### Explanation:

Here you have a bloc of solid aluminium and you heat it up to reach the temperature of fusion and then you supply a bit more of heat to completely melt it.
So in total you have:
${Q}_{1} + {Q}_{2} =$
Where:

${Q}_{1} = m {c}_{\text{Al}} \Delta T$ is the heat needed to heat up your bloc from ${580}^{\circ} C$ to ${660.4}^{\circ} C$

${Q}_{2} = m {L}_{f}$ is the heat needed not to increase its temperature but to melt it completely.

We have:

${Q}_{1} + {Q}_{2} = m {c}_{\text{Al}} \Delta T + m {L}_{f} =$

$= 10 \cdot 0.89 \cdot \left(660.4 - 580\right) + 10 \cdot 398 = 4695.6 J$