Question

The temperature of 15.71 grams of gold rises from 32°C to 1,064°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?

Answer 1

Hello!

The answer is:

The total energy gained is equal to 3091 Joules.

Why?

To calculate how much energy is gained by the gold, we need to use the formula to calculate the heat transfer, it's defined by the following equation:

$Q=mc\Delta T$

We know that the gold melts completely (it reached its melting point or fusion temperature), so, we need to rewrite the equation as follow:

$Q=mc\Delta T+m\Delta H_{fusion}$

Where,

m,is the mass of the material

c, is the specific heat of the material

ΔT, is the change of temperature.

ΔH, is the heat of fusion of the material.

So, from the statement we know the following information:

$m=15.74grams\\\\\Delta T=1064\°C-32\°C=1032\°C\\\\c=0.1291\frac{Joules}{gram\°C}\\\\m\Delta H_{fusion=15.71grams*\frac{63.5Joules}{gram}=997.59Joules$

Then, substituting and calculating, we have:

$Q=mc\Delta T+m\Delta H_{fusion}$

$Q=15.71grams*0.1291\frac{Joules}{gram\°C}*1032\°C+997.59Joules$

$Q=2093.06Joules+997.59Joules=3090.65Joules=3091Joules$

Hence, we have that the total energy gained is equal to 3091 Joules.

Have a nice day!