Question

A ceramic container used for melting metals (called a crucible) contains 1.30 kg of a molten metal. The liquid metal cools until it reaches its melting point of 1,749°C. A scientist then measures that 2.99 ✕ 10^4 J of heat is transferred out of the metal before it completely solidifies. What is the latent heat of fusion of this metal, in J/g? (Be careful with units!)

Answer 1

23 J/g

Step-by-step explanation:

The heat transferred in a phase change like this case is calculated as:

`Q=mH_f`

Where m is the mass and Hf is the latent heat of fusion. We can solve the equation for Hf

`H_f=(Q)/(m)`

Now, replacing Q = 2.99 x 10⁴ J and the mass = 1300 g, we get:

`H_f=\frac{2.99*10^4J}{1300\text{ g}}=23\text{ J/g}`

We use 1300 g instead of 1.30 kg because we want the units in J/g.

Therefore, the latent hear of fusion of this metal is 23 J/g