What is the average kWh/d per person in Sydney due to aluminium smelting?

Question

Tomago aluminium smelter located near Sydney has a rated capacity of 520,000 tonnes of aluminium per year. The production of each kilogram of aluminium requires 15 kWh of primary energy to smelt from alumina. Assume the primary energy needed to run the smelter was divided among the population of Sydney (approx. 500,000). What is the average kWh/d per person in Sydney due to aluminium smelting?

Answer 1

This one has a lot to keep track of. So we want to know the average Energy output, per day, per person. So let's start with what we know.

 

1) It takes 15 kWh of energy to smelt 1 kg of aluminium.

2) 520,000 tonnes of aluminium are smelted per year. The unit tonne is equivalent to 1000 kg.

3) The population of Sydney is approximately 500,000.

 

So if we multiply the energy to smelt 1 kg of aluminium by the amount of aluminium smelted in a year (expressed in kg), that will give us the energy needed to smelt a years' worth of aluminium. Since the problem is asking for energy needed per day, just divide that result by 365 days/year. "Per person" means we want to divide now by the population of Sydney.

 

In summary, the average kWh/day per person is (15 kWh/kg)*(520,000 tonnes/yr)*(1000 kg/tonne)/(365 days/yr)/(500,000 people)