Additional Math Pages & Resources

Wednesday, January 25, 2012

Full, Fuller or Fullest?

Today I filled my car with gasoline and put 19.660 gallons into an 18.5 gallon tank. How? This is a test for your elementary math.

Please select any answers that apply:
  1. The owner's manual is incorrect (the tank holds more than 18.5 gallons)
  2. The gas pump metering is incorrect (I got charged for more fuel than was delivered)
  3. Some of the fuel leaked onto the ground or elsewhere out of the tank
 I am happy to report that any of these, and many other reasons may apply. Let's take the 3 choices one by one.

1. Technically the owner's manual is correct, BUT the tank does hold more than 18.5 gallons. All fuel tanks on US motor vehicles have an expansion space that accomodates fuel expansion and vapors. This ranges from 10-12% of the total space of the tank, so my car might have an extra 2 gallons or so of space. Normally this does not fill with fuel, due to automatic shut-off valves that sense when the tank is nearly full. I was holding the handle to fill it up, and the pump did not stop.
I know a bit about fuel venting, because in a former career, I created products like Mitchell Automechanics and an Emission Control Training Manual, and other fascinating books that deal with automotive evaporative control systems (they keep fuel vapors from polluting our air).

2.  The station I filled up at was using a pump that does not adjust volume to compensate for temperature variations. A label on the pump says "This device dispenses gasoline solely by volume measured in standard gallons (231 cubic inches). It does not adjust for temperature or other factors which may affect the energy content of each gallon dispensed."   

This means I should have received an accurate number of gallons, but I might not have received the full amount of energy that is contained in fuel at the standard 60 degrees F. My fuel may have been hotter or colder (holding more or less energy) than I expected. This is a complex subject to grasp - visit this site for a clear (if long) explanation.

Alternatively, the pump might have been defective and dispensing the incorrect amount of fuel. But it's unlikely, as they are frequently checked.

3. Some of the fuel did leak out of the tank and land on the ground. Not much, but a little. Let's say 3-4 ounces (half a cup), or a small fraction of a gallon. It also spilled down the side of the car and stained the plastic trim. The attendant at the station hosed down the fuel spill and gave me some wipes to clean the car. I didn't take a picture of the spilled fuel, but the car looks OK.

Let's end with a simple question:

Is it possible to fill a container with more than it was supposed to contain?

Yes. Absolutely. We prove this every Thanksgiving meal when we eat more than we should!

PS You might wonder if the fuel tank can expand and contract like your stomach does. To a limited extent, yes, it can change its shape and volume when subjected to enough pressure or vacuum.