Log out Go to App
Go to App

Learning Materials

Features

Discover

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.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Proven remaining reserves of oil, gas, and coal are 10,8, and \(20 \mathrm{ZJ},{ }^{88}\) while we have used 8,4, and \(8 \mathrm{ZJ}\) of each. What fraction of the original total fossil fuel resource have we already used, then?

If the inevitable decline in fossil fuel availability is a potentially important disrupter of the status quo in the decades to come, what are some reasons it gets little attention compared to, say, climate change? No right answer here, but what do you think contributes?

It is hard for many people to appreciate that fossil fuels will not just "run out one day," because they don't appreciate the substantial amount of work that must go into extracting the resource from a reluctant ground. What common, day-to-day personal experiences do you imagine contributes to this disconnect? \(^{89}\)

One liter of gasoline \((1,000 \mathrm{~mL})\) has a mass of about \(750 \mathrm{~g}\) and contains about \(9.7 \mathrm{kWh}\) of energy. Meanwhile, a typical AA battery occupies \(7.4 \mathrm{~mL}\) of volume at a mass of \(23 \mathrm{~g}\), while holding about \(0.003 \mathrm{kWh}\) of energy. How much volume and how heavy would a collection of AA batteries be in order to match the energy in a liter of gasoline, and by what factors (in volume and mass) is gasoline superior?

Putting the cheapness of fossil fuels into perspective, a gallon of gasoline purchased for \(\$ 4\) might deliver \(6 \mathrm{kWh}\) of mechanical energy after accounting for efficiency of the associated engine. A laborer might be expected to export \(100 \mathrm{~W}\) of mechanical power, on average, and be limited to 8 hours per day. How many hours would it take for the laborer to accomplish the equivalent output of a gallon of gasoline? At a rate of \(\$ 15 / \mathrm{hr}\), how much will this cost you?
See all solutions

Recommended explanations on Environmental Science Textbooks

Ecology Research

Read Explanation

Energy Resources

Read Explanation

Biological Resources

Read Explanation

Sustainability

Read Explanation

Physical Environment

Read Explanation

Environmental Policy

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free