Final answer:
To calculate how far one could pedal a bicycle using the energy from 3 gallons of gasoline, the chemical energy in the gasoline is converted to work at an assumed efficiency rate of 25%. Considering a constant power output of 100 Watts to maintain a speed of 15 km/h, one could bike approximately 4,062.5 kilometers on that amount of energy.
Step-by-step explanation:
To solve the problem of how far one could bicycle using the energy in 3 gallons of gasoline, we first need the energy content of gasoline. Given that 1 gallon of gasoline contains about 130 MJ (Megajoules) of chemical energy, 3 gallons would contain 390 MJ of energy (3 x 130 MJ).
To find the distance that can be biked, we need to determine the amount of energy expended by biking. A rough estimate of human efficiency at converting food to work is about 25%. If we assumed a similar efficiency of converting gasoline to work, 390 MJ would become 97.5 MJ of useful work (25% of 390 MJ).
We next need to consider the power (rate of energy usage) required to bike at 15 km/h. This will vary based on factors like wind resistance, rolling resistance, rider’s weight, and the efficiency of the bicycle, but as an example, if it takes 100 W (watts) to sustain this speed, we can use the formula:
Energy (Joules) = Power (Watts) x Time (Seconds)
So, the time (in seconds) that one could bike using 97.5 MJ would be:
Time = 97.5 MJ / 100 W = 975,000,000 J / 100 J/s = 9,750,000 s
To find the distance, we convert the time to hours and multiply by the speed:
Distance = (9,750,000 s / 3600 s/h) x 15 km/h = 4,062.5 km
Therefore, assuming an efficiency of 25% in converting gasoline to work and a constant power output of 100 W, one could theoretically bike 4,062.5 km on 3 gallons of gasoline.