A world record was set in Eco-Marathon by a french team in 2003 called Microjoule with a performance of 10,705 miles per gallon. The microjoule runs on ethanol. If the cars are given 100 grams of ethanol (specific gravity = .789) and drive until the fuel runs out, how far did the microjoule drive in kilometers?
Any help is greatly appreciated!
To calculate the distance the Microjoule drove in kilometers, we need to use the following steps:
Step 1: Convert the mass of ethanol from grams to liters.
The specific gravity of ethanol is given as 0.789, which means that 1 liter of ethanol weighs 0.789 kilograms (789 grams). To convert the given mass of 100 grams to liters, we divide it by the density:
100 grams / 789 grams/liter ≈ 0.127 liters
Step 2: Calculate the volume of ethanol in gallons.
To convert liters to gallons, we can use the conversion factor of 1 gallon = 3.78541 liters:
0.127 liters × (1 gallon / 3.78541 liters) ≈ 0.034 gallons
Step 3: Calculate the distance driven in miles.
The Microjoule achieved a performance of 10,705 miles per gallon. Therefore, we multiply the volume of ethanol in gallons by the performance:
0.034 gallons × 10,705 miles/gallon ≈ 365.17 miles
Step 4: Convert the distance from miles to kilometers.
To convert miles to kilometers, we use the conversion factor of 1 mile = 1.60934 kilometers:
365.17 miles × 1.60934 kilometers/mile ≈ 587.46 kilometers
Therefore, the Microjoule drove approximately 587.46 kilometers.