QQuestionEngineering
QuestionEngineering
Estimate a typical gas mileage (in miles/gallon).
How many gallons does it take to go 1 mile?
Estimate the energy in a gallon of gas (in joules).
How many joules does it take to go 1 mile?
Estimate the energy of a human heartbeat (in joules).
Estimate how many human heartbeats it would take to drive a car 1 mile.
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Answer
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Step 1:I'll solve this problem step by step, using precise estimates and LaTeX formatting:
Step 2:: Estimate Gas Mileage
- Typical car gets around $$25 \text{ miles/gallon}
- Inverse of this is \frac{1}{25} = 0.04 \text{ gallons/mile}
Step 3:: Gallons per Mile
- Confirmed estimate: $$0.04 \text{ gallons/mile}
Step 4:: Energy in a Gallon of Gas
- One gallon of gasoline contains approximately $$1.3 \times 10^{8} \text{ joules}
Step 5:: Energy to Drive 1 Mile
- Energy per mile = $$0.04 \text{ gallons/mile} \times (1.3 \times 10^{8} \text{ joules/gallon})
- = 5.2 \times 10^{6} \text{ joules/mile}
Step 6:: Energy of a Human Heartbeat
- Typical heartbeat energy: approximately $$1 \text{ joule}
Step 7:: Heartbeats to Drive 1 Mile
- $$\frac{5.2 \times 10^{6} \text{ joules/mile}}{1 \text{ joule/heartbeat}} = 5.2 \times 10^{6} \text{ heartbeats/mile}
Final Answer
- Gas Mileage: 25 \text{ miles/gallon} - Gallons per Mile: 0.04 \text{ gallons/mile} - Energy per Mile: 5.2 \times 10^{6} \text{ joules/mile} - Heartbeats to Drive 1 Mile: 5.2 \times 10^{6} \text{ heartbeats}
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