# Which energy is saved by recycling? The case of Aluminium

In this little exercise, we will compare the energy for remelting aluminium from a casing of a phone to that from extracting aluminium from its oxide.

We will compare the energy to remelt 1 kg of aluminium from the battery casings of smartphones during recycling to that of extracting 1 kg of aluminium from aluminium oxide assumed to be its ore.

## 1. Let us estimate the energy needed to re-melt 1 kg of aluminium .

#### Assumptions:

We start at (T_{room} = 298 K) and heat the aluminium up to its melting temperature (T_{melt} = 933 K) then we melt it.

#### Input:

Mass Al (m = 1 kg)

Melting point of Al (T_{melt} = 933 K)

Mass calorific capacity (C_p(Al) = 900 J/(kg K))

Molar melting enthalpy (∆H_m(Al) = 10.5 kJ/mol =10500 J/mol)

Atomic weight (W_{Al} = 26.98 g/mol) (average)

#### Thermodynamic hints:

• The energy needed to heat Al(s) up to the melting point:

[E_{heat} = C_p (Al)(T_{melt} – T_{room})]

• The energy needed to melt 1 kg = 1000 g of Al (s) at the melting point:

[E_{melt} = Delta H_f (Al)* 1000 / W_{Al}]

Calculation:
The total energy needed to remelt aluminium is

[E= E_{heat}+E_{melt}]

the calculation gives:

[E= 900 (frac{J}{kg.K}).(933-298) (K) +frac{10500(frac{J}{mol}) . 1000 (frac{g}{kg})}{27.98 (frac{g}{mol})}]

we find (E= 961 kJ/kg)

## 2. Let us estimate the energy needed to extract 1 kg of Al from Al2O3

The reaction is:

(Al_2O_3 rightarrow 2 Al+frac{3}{2}O_2) (reaction 1)

with a reaction enthalpy of

[Delta G(T) =1.676.10^6 – 320 T (J)]

#### Assumptions:

Reaction temperature T = 298 K

Process is 100% efficient

#### Calculation for the reduction of aluminium oxide:

At room temperature (298 K) the molar enthalpy needed for reaction 1 is

(Delta G(298K) =1.676.10^6 – 320* 298 = 1.59 MJ) (per 2 mol of Al)

The energy needed to extract 1 kg of aluminium from its oxide is

[E_{ext}= frac{ 1.59 (frac{MJ}{mol})*1000 (frac{g}{kg})}{2 mol(Al)*26.98 (frac{g}{mol}) }=29.5 frac{MJ}{kg}=29500 frac{kJ}{kg}]

## 3. Compare the energy used in both processes and estimate which one is the less energy consuming.

Its costs:

29,500 kJ/kg to extract Al from its oxide

versus 961 kJ/kg to re-melt used Al