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Chapter 8: Problem 17

A gallon of gasoline contains about \(37 \mathrm{kWh}\) of energy and costs about \(\$ 4\), while a typical AA battery holds about \(0.003 \mathrm{kWh}\) and costs about \(\$ 0.50\) each, in bulk. By what factor are batteries more expensive, for the same amount of energy?

Short Answer

Expert verified
Short Answer: AA batteries are approximately 3083 times more expensive than gasoline for the same amount of energy.

Step by step solution

01

Calculate cost per kWh of gasoline

To find the cost per kWh for gasoline, we need to divide the cost of one gallon of gasoline by the energy it contains: Cost per kWh (Gasoline) = \(\frac{\text{Cost of one gallon}}{\text{Energy in one gallon}}\) Cost per kWh (Gasoline) = \(\frac{\$4}{37 \mathrm{kWh}}\)
02

Calculate cost per kWh of AA battery

To find the cost per kWh for an AA battery, we need to divide the cost of one AA battery by the energy it contains: Cost per kWh (AA Battery) = \(\frac{\text{Cost of one AA battery}}{\text{Energy in one AA battery}}\) Cost per kWh (AA Battery) = \(\frac{\$0.50}{0.003 \mathrm{kWh}}\)
03

: Step 3: Calculate the factor by which batteries are more expensive

: To find the factor by which batteries are more expensive, we need to divide the cost per kWh of an AA battery by the cost per kWh of gasoline: Factor = \(\frac{\text{Cost per kWh (AA Battery)}}{\text{Cost per kWh (Gasoline)}}\) Factor = \(\frac{\frac{\$0.50}{0.003 \mathrm{kWh}}}{\frac{\$4}{37 \mathrm{kWh}}}\) Factor = \(\frac{(\$0.50)(37 \mathrm{kWh})}{(0.003 \mathrm{kWh})(\$4)}\) Now, let's perform the calculations: Factor = \(\frac{(0.50)(37)}{(0.003)(4)}\) Factor ≈ 3083.33 So batteries are approximately 3083 times more expensive than gasoline for the same amount of energy.

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Most popular questions from this chapter

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