Question

How much energy does it take to make 500 g of solid lead at 21°C and turn it entirely to liquid lead?

Answer 1

The total amount of energy required to turn solid lead entirely to liquid lead consists of two parts:

$$Q_{tot} = Q_{heat} + Q_{melt}$$

where $Q_{heat}$ is the energy required to heat lead up to the melting point and $Q_{melt}$ is the energy requred to melt the given amount of lead.

The first term:

$$Q_{heat} = mc(T_{melt}-T_0)$$

where $m = 0.5 kg$ is the mass of lead, $c = 127.5 \dfrac{J}{kg\cdot K}$ is the specific heat capacity of lead,$T_{melt} = 600.6 K$ is the melting point of lead and $T_0 = 294.2 K$ is the initial temperature (21°C).

Substitute numerical values:

$$Q_{heat} = mc(T_{melt}-T_0) = 0.5\cdot 127.5\cdot (600.6 - 294.2) = 19.533 kJ$$

The second term:

$$Q_{melt} = m\lambda$$

where $\lambda = 25 kJ/kg$ is the specific heat of fusion of lead.

Substitute numerical values:

$$Q_{melt} = m\lambda = 0.5\cdot 25 = 12.5 kJ$$

The total energy, thus, will be:

$$Q_{tot} = 19.533 kJ + 12.5 kJ = 32.033 kJ \approx32 kJ$$

Answer. It takes 32 kJ to make 500 g of solid lead at 21°C and turn it entirely to liquid lead.