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Chapter 8: Problem 15

What if we could get our energy from drinking gasoline? \(^{82}\) Referring to Table \(8.2\), how many grams of gasoline \(^{83}\) would we have to drink daily to satisfy the typical 2,000 kcal/day diet? How much volume does this represent if gasoline is \(0.75 \mathrm{~g} / \mathrm{mL}\) ? Relate this to a familiar container for holding liquids. 8

Short Answer

Expert verified
Answer: You would have to drink about 0.243 mL, or 1/20 of a teaspoon, of gasoline daily to satisfy a 2,000 kcal/day diet.

Step by step solution

01

Convert kcal to Joules

First, we need to convert the 2,000 kcal/day diet into Joules. We know that 1 kcal equals 4,184 J. Therefore, multiplying the given kcal by the conversion factor, we get: \( 2000 \; \mathrm{kcal/day} \times \dfrac{4184 \; \mathrm{J}}{1 \; \mathrm{kcal}} = 8,368,000 \; \mathrm{J/day} \)
02

Calculate the mass of gasoline

Next, we need to find out how many grams of gasoline are required to provide the energy needed. We are given that the energy content of gasoline is \(4.6\times10^7 \mathrm{J/g}\). Therefore, the mass of gasoline required can be calculated by dividing the energy needed by the energy content of gasoline: \( m_g = \dfrac{8,368,000 \mathrm{J}}{4.6\times10^7 \mathrm{J/g}} = 0.182 \; \mathrm{g} \)
03

Calculate the volume of gasoline

Now that we have the mass of gasoline required, we can calculate the volume it will occupy using the given density of gasoline. We are given that gasoline has a density of 0.75 g/mL. Therefore, dividing the mass of gasoline by the density, we get the volume required in mL: \( V_g = \dfrac{0.182 \; \mathrm{g}}{0.75\mathrm{g/mL}} = 0.243 \; \mathrm{mL} \)
04

Relate the volume to a familiar container

The volume we obtained is 0.243 mL, which is equal to around 0.05 teaspoons. Therefore, we would have to drink a very small amount of gasoline – just 1/20 of a teaspoon daily – to satisfy a 2,000 kcal/day diet.

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Most popular questions from this chapter

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