# How many joules of heat are required to melt a 55.0-g ice cube at 0°C?

Jul 15, 2016

$\text{18,300 J}$

#### Explanation:

In order to be able to answer this question, you must know the value of water's enthalpy of fusion, $\Delta {H}_{\text{fus}}$, which is listed as

$\Delta {H}_{\text{fus" = "33.55 J g}}^{- 1}$

https://en.wikipedia.org/wiki/Enthalpy_of_fusion

Now, a substance's enthalpy of fusion tells you how much heat is needed in order to convert $\text{1 g}$ of said substance from solid at its melting point to liquid at its melting point.

In water's case, an enthalpy of fusion equal to ${\text{333.55 J g}}^{- 1}$ tells you that $\text{1 g}$ of ice at ${0}^{\circ} \text{C}$ can be converted to $\text{1 g}$ of liquid water at ${0}^{\circ} \text{C}$ by supplying $\text{333.55 J}$ of heat.

Your ice cube has a mass of $\text{55.0 g}$, which means that it will require

55.0 color(red)(cancel(color(black)("g"))) * overbrace("333.55 J"/(1color(red)(cancel(color(black)("g")))))^(color(blue)( = DeltaH_"fus")) = "18,345.25 J"

Rounded to three sig figs, the number of sig figs you have for the mass of the ice cube, the answer will be

"heat needed" = color(green)(|bar(ul(color(white)(a/a)color(black)("18,300 J")color(white)(a/a)|)))