# Question #7c785

Feb 21, 2018

$170000000 \text{kJ}$, or $170000 \text{MJ}$

#### Explanation:

We know that the mass of the material is directly proportional to the amount of energy needed. Where $m$ is the mass and $q$ the energy, we can write:

$q \propto m$. Using this, we have two methods to answer the question.

Method 1
$q = m {L}_{f}$, where ${L}_{f}$ is a constant.

What is ${L}_{f}$, this constant? It is the specific latent heat of fusion, defined as is the heat needed to change a mass of $1 \text{kg}$ the substance from a solid at its melting point into liquid at the same temperature.

So we can write that ${L}_{f} = \frac{q}{m}$

Here, $m = 0.085 \text{kg}$ and $q = 8.5 \times {10}^{4} \text{J}$. Inputting:

${L}_{f} = \frac{8.5 \times {10}^{4}}{0.085}$

${L}_{f} = 1000000 \text{J/kg}$, or $1000 \text{kJ/kg}$

In the second situation, $m = 170000 \text{kg}$

We know that $q = m {L}_{f}$. We simply input:

$q = 170000 \cdot 1000 = 170000000 \text{kJ}$, or $170000 \text{MJ}$

Method 2
We know that $q \propto m$, and it follows that ${q}_{1} / {m}_{1} = {q}_{2} / {m}_{2}$, or:

${q}_{1} {m}_{2} = {q}_{2} {m}_{1}$

We simply input the values needed:

$85 \cdot 170000 = 0.085 {q}_{2}$

$14450000 = 0.085 {q}_{2}$

${q}_{2} = \frac{14450000}{0.085}$

${q}_{2} = 170000000 \text{kJ}$, or $170000 \text{MJ}$