Question

It takes \(15 \mathrm{kWh}\) (kilowatt-hours) of electrical energy to produce 1.0 kg aluminum metal from aluminum oxide by the HallHeroult process. Compare this to the amount of energy necessary to melt \(1.0 \mathrm{~kg}\) aluminum metal. Why is it economically feasible to recycle aluminum cans?

Short answer

The energy required to produce 1.0 kg of aluminum from aluminum oxide is \(54 \times 10^6\) joules, while the energy required to melt 1.0 kg of aluminum is only \(3.97 \times 10^5\) joules. This significant difference in energy consumption makes recycling aluminum cans economically feasible, as it saves about \(54 \times 10^6 - 3.97 \times 10^5\) joules per kg of aluminum. This results in lower production costs and less environmental impact, making aluminum can recycling an economically and environmentally friendly option.

Step-by-step solution

Finding the energy required to produce aluminum from aluminum oxide

We are given that it takes 15 kWh of electrical energy to produce 1.0 kg of aluminum from aluminum oxide by the Hall-Heroult process.

Converting energy units to joules

To compare the energy required for production and melting, we need to convert the energy used to produce aluminum from aluminum oxide to joules. We know that 1 kWh equals 3.6 x 10^6 J. So, we have: \[ 15\, \text{kWh} \times \frac{3.6 \times 10^6 \, \text{J}}{1\, \text{kWh}} = 54 \times 10^6 \, \text{J} \] Hence, the energy required to produce 1.0 kg of aluminum from aluminum oxide is \(54 \times 10^6\) joules.

Calculate the energy required to melt aluminum

To calculate the energy required to melt 1.0 kg of aluminum, we need to find the specific heat of fusion for aluminum. The specific heat of fusion for aluminum is 3.97 x 10^5 J/kg. Now we can calculate the energy required to melt 1.0 kg aluminum using the formula: \[ \text{Energy} = \text{mass} \times \text{specific heat of fusion} \] \[ \text{Energy} = 1.0 \, \text{kg} \times 3.97 \times 10^5 \frac{\text{J}}{\text{kg}} = 3.97 \times 10^5 \, \text{J} \] So, the energy required to melt 1.0 kg of aluminum is \(3.97 \times 10^5\) joules.

Compare the energy required for production and melting

Now, we will compare the energy required to produce 1.0 kg aluminum and the energy required to melt 1.0 kg aluminum: Energy for production: \(54 \times 10^6\) J Energy for melting: \(3.97 \times 10^5\) J The energy required to produce aluminum from aluminum oxide is significantly greater than the energy required to melt aluminum.

Discuss the economic feasibility of recycling aluminum cans

Recycling aluminum cans is economically feasible because melting aluminum requires much less energy compared to producing aluminum from aluminum oxide. Recycling aluminum cans saves about \(54 \times 10^6 - 3.97 \times 10^5\) joules per kg of aluminum, which translates to lower production costs and less impact on the environment. This energy savings makes recycling aluminum cans an economically and environmentally friendly option.

Key concepts

Energy Conservation in Aluminum Production

Energy conservation is a critical aspect of aluminum production due to the high energy requirements of the Hall-Heroult process. This primary industrial method for extracting aluminum from its oxide requires approximately 15 kWh of electrical energy to produce just 1.0 kg of aluminum metal. To put this into perspective, converting this energy requirement into joules using the conversion rate that 1 kWh equals 3.6 x 10^6 J, results in a staggering 54 x 10^6 J of energy required for the production of a single kilogram of aluminum.

Given the immense energy expenditure involved, manufacturers and environmentalists alike look for ways to reduce energy consumption. One method is through technological advancements that enhance the efficiency of the Hall-Heroult process. Another is by amplifying energy-saving efforts through the recycling of aluminum products, which significantly decreases the need for energy-intensive raw aluminum production. Energy conservation not only lowers the manufacturing cost, making the process more economically viable but also contributes to a reduction in the carbon footprint of aluminum production, aiding in the global effort to combat climate change.

Specific Heat of Fusion

Understanding the specific heat of fusion is pivotal when it comes to materials like aluminum. It is defined as the amount of energy required to change a substance from the solid phase to the liquid phase without a change in temperature. For aluminum, this energy value is 3.97 x 10^5 J/kg. The specific heat of fusion comes into play when melting aluminum for recycling purposes. Comparatively, the energy required to melt existing aluminum metal is substantially lower than producing new metal from ore.

Utilizing the equation \(Energy = mass \times specific heat of fusion\), we calculate that melting 1.0 kg of aluminum necessitates 3.97 x 10^5 J. This figure pales in comparison to the energy inputs required for production, reaffirming the energy-conscious approach of melting and reusing aluminum rather than manufacturing it anew. As educators, it is important to highlight this distinction to students as it illustrates a practical application of thermodynamic principles in industry and environmental stewardship.

Environmental Benefits of Recycling Aluminum

The recycling of aluminum extends well beyond simple economics. From an environmental perspective, the benefits are immense. As demonstrated in the exercise, the production of new aluminum from bauxite ore consumes a large amount of energy, roughly 54 x 10^6 J per kilogram. In contrast, recycling aluminum requires just a fraction of that energy, approximately 3.97 x 10^5 J per kilogram.

This drastic difference not only implies significant energy savings but also means a reduction in greenhouse gas emissions, less mining of bauxite ore, and conservation of natural resources. Moreover, since aluminum can be recycled indefinitely without loss of quality, it underscores the sustainable cycle that can be achieved.

• Reduces landfill waste: Recycling aluminum keeps it out of the waste stream, decreasing the pressure on landfill sites.
• Conserves energy: Recycling uses about 95% less energy than new production, translating to significant conservation of electricity and fossil fuels.
• Minimizes pollution: Less energy use results in fewer emissions, mitigating air and water pollution.

Educating students on these benefits instills awareness and encourages responsible consumption and recycling habits, fostering a more sustainable future.