Approximately 220 million tires are discarded in the U.S. each year. These tires present a disposal problem because they take up space, harbor pests, and have been known to catch fire. One tire can generate about 250,000 BTUs (1 BTU = 3 x 10 -4 kWh) when it is burned. The average American home consumes about 10,000 kWh of electricity per year. How many tires would be needed to meet the annual electricity demand of ten homes for one year if the production of electricity from tires is 50% efficient?

According to the Second Law of Thermodynamics, only a part of generated energy when tires are burned can be utilized due to irreversibilities associated with finite temperature differences. The energy from a tire that can be transformed into electricity ([tex]E_{out}[/tex]), measured in kilowatt-hours, is estimated by definition of efficiency:

[tex]E_{out} = \eta \cdot E_{in}[/tex]

Where:

[tex]\eta[/tex] - Efficiency, dimensionless.

[tex]E_{in}[/tex] - Energy liberated by burning, measured in kilowatt-hours.

Given that [tex]\eta = 0.5[/tex] and [tex]E_{in} = 75\,kWh[/tex], the amount of energy per year generated by a tire is:

[tex]E_{out} = 0.5\cdot (75\,kWh)[/tex]

[tex]E_{out} = 37.5\,kWh[/tex]

Now, the amount of tires needed to meet the demand of then homes for one year is:

[tex]n = \frac{(10\,homes)\cdot \left(10000\,\frac{kWh}{home} \right)}{37.5\,\frac{kWh}{tire} }[/tex]

[tex]n = 2666.667\,tires[/tex]

2667 tires are needed to meet the demand of ten homes for one year.