Question

A goldsmith melts 12.4 grams of gold to make a ring. The temperature of the gold rises from 26°C to 1064°C, and then the gold melts completely. If gold’s specific heat is 0.1291 joules/gram degree Celsius and its heat of fusion is 63.5 joules/gram, how much energy is gained by the gold?

The gold gains a total of ____ joules of energy.

I was given this by somebody. No idea what to do with this.
QJ=(12.4g*(1064-26)°C*0.1291J/g/°C)+(12.4g*63.5J)

Answer 1

The gold gains a total of 2.468 kilo-joules of energy.

Step-by-step explanation:

Total heat or energy gained by the gold is equal to heat applied and heat required to melt the gold completely.

Total energy = Q+ Q'

Heat of fusion of gold =
`\Delta H_(fus) =63.5 joules/gram`

Mass of gold melted ,m= 12.5 g

Specific heat of gold ,c= 0.1291 joules/gram °C

Change in temperature = ΔT = 1064°C - 26°C = 1038 °C

Heat of applied to the gold = Q

`Q=mc\Delta T`

`Q'=\Delta H_(fus)* m`

Total energy = Q+ Q'

`=12.5 g* 0.1291 joules/gram ^oC* 1038 ^oC+63.5 joules/gram* 12.5 g`

= 2,468.82 Joule= 2.468 kilo-Joule

The gold gains a total of 2.468 kilo-joules of energy.