Question

Question #09ac6

Answer 1

`1.0 * 10^2"kJ"`

Explanation:

You can find the latent heat of fusion, also referred to as the enthalpy of fusion, `DeltaH_"fus"`, for gold listed here

`DeltaH_"fus" = "63 kJ kg"^(-1)`

http://www.engineeringtoolbox.com/fusion-heat-metals-d_1266.html

So, a substance's enthalpy of fusion tells you how much heat is required in order to melt `"1 kg"` of that substance.

In your case, gold is said to have an enthalpy of fusion equal to `"67 kJ kg"^(-1)`. This tells you that in order to melt `"1 kg"` of gold, i.e. go from solid gold at its melting to liquid gold at its melting point, you must provide it with `"67 kJ"` of heat.

You're dealing with a `"1.5-kg"` sample of gold, which means that you'll need

`1.5 color(red)(cancel(color(black)("kg"))) * overbrace("67 kJ"/(1color(red)(cancel(color(black)("kg")))))^(color(blue)(DeltaH_"fus")) = "100.5 kJ"`

Rounded to two sig figs, the number of sig figs you have for the mass of gold, the answer will be

`"energy required" = color(green)(|bar(ul(color(white)(a/a)color(black)(1.0 * 10^(2)"kJ")color(white)(a/a)|)))`