# Question #4329b

Apr 20, 2015

The equation you're interested in describes the energy (in the form of heat) needed to change the state of a substance from solid to liquid.

$q = m \cdot \Delta H$, where

$m$ - the mass of the substance;
$\Delta H$ - the enthalpy of fusion, which describes the heat required to change the state of 1 gram of a substance from solid to liquid.

Notice that the equation lacks a term that describes a change in temperature ($\Delta T$); that happens because the enthalpy of fusion is a latent heat, i.e. the heat absorbed by a substance during a constant temperature process.

In your case, the enthalpy of fusion applies to substances at their melting points.

Here's how you'd use this in a problem. Let's say you want to calculate the energy required to transform 20.0 g of ice at ${0}^{\circ} \text{C}$ to liquid water at ${0}^{\circ} \text{C}$ $\to$ perform a phase change.

The enthalpy of fusion for water is listed as $\text{334 J/g}$. This means that you need to provide 334 J for every gram of water to get to go from solid to liquid at constant temperature.

$q = m \cdot \Delta H$

$q = 20.0 \cancel{\text{g") * 334"J"/cancel("g") = color(green)("6680 J}}$

That's the energy 20.0 g of water needs in order to go from solid (ice) to liquid.