Question

The energy used to compress air in the United States is estimated to exceed one-half quadrillion \(\left(0.5 \times 10^{15}\right)\) kJ per year. It is also estimated that 10 to 40 percent of the compressed air is lost through leaks. Assuming, on average, 20 percent of the compressed air is lost through air leaks and the unit cost of electricity is \(\$ 0.13 / \mathrm{kWh}\), determine the amount and cost of electricity wasted per year due to air leaks.

Short answer

Answer: The cost of electricity wasted per year due to air leaks in the United States is $3.611 x 10^9.

Step-by-step solution

Determine the energy lost due to air leaks

Initially, we are given the total energy used to compress air in the United States, which is 0.5 x 10^15 kJ. To calculate the energy loss due to air leaks, we need to find 20% of this total energy, as mentioned in the problem. Energy loss = (Total energy used to compress air) x (Percentage loss due to air leaks)

Calculate the energy loss due to air leaks

To find out the energy loss, we will multiply the total energy by the percentage of air leaks. Energy loss = \(\left(0.5 \times 10^{15}\right) \times \frac{20}{100}\) Energy loss = \(\left(0.5 \times 10^{15}\right) \times 0.20\) Energy loss = \(1 \times 10^{14}\) kJ Now we have found the energy loss due to air leaks, which is 1 x 10^14 kJ.

Convert energy loss from kJ to kWh

Next, we need to convert the energy loss from kJ to kWh since the cost of electricity is given in $/kWh. 1 kJ = 0.000277778 kWh, so we can convert the energy loss using the following formula. Energy loss (kWh) = Energy loss (kJ) × Conversion factor

Calculate the energy loss in kWh

Using the conversion factor, we can determine the energy loss in kWh. Energy loss (kWh) = \(1 \times 10^{14}\) kJ × 0.000277778 kWh/kJ Energy loss (kWh) = \(2.777 \times 10^{10}\) kWh Now we have found the energy loss in kWh, which is 2.777 x 10^10 kWh.

Calculate the cost of wasted electricity

Finally, we need to calculate the cost of the wasted electricity. The unit cost of electricity is given as $0.13/kWh, so we can simply multiply the energy loss (kWh) by the unit cost to obtain the cost of wasted electricity. Cost of wasted electricity = Energy loss (kWh) × Unit cost of electricity Cost of wasted electricity = \(2.777 \times 10^{10}\) kWh × \(0.13 / \mathrm{kWh}\) Cost of wasted electricity = \(3.611 \times 10^9\) Therefore, the cost of electricity wasted per year due to air leaks is $3.611 \times 10^9.