Question

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

Answer 1

`"18,300 J"`

Explanation:

In order to be able to answer this question, you must know the value of water's enthalpy of fusion, `DeltaH_"fus"`, which is listed as

`DeltaH_"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 `"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 `"333.55 J g"^(-1)` tells you that `"1 g"` of ice at `0^@"C"` can be converted to `"1 g"` of liquid water at `0^@"C"` by supplying `"333.55 J"` of heat.

Your ice cube has a mass of `"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)|)))`