One morning Don’s car ran out of gasoline in a deserted area. He hiked to the ne

Question

One morning Don’s car ran out of gasoline in a deserted area. He hiked to the nearest gas station, reaching it during the hottest part of the day. Upon reaching the station, he ?lled up a 14 gallon container with gasoline and started his walk back. By the time he reached his car in the evening, the temperature had dropped 30.0289 ?F. How many gallons of gasoline did Don have when he reached his car? The volume expansion of gasoline is ß = 0.00096 (?C)^-1. Neglect the change in volume of the container.

Answer in units of gallons

Please show ALL STEPS to completing this problem! Thank you so much.

Explanation / Answer

First, convert to standard units (Conversion back to gallons at the end)

14 gallons X 3.786 X 10-3 m3/gal = .053004 m3

The change is temp F to change in temp C

C = (5/9)(F) = (5/9)(30.0289) = 16.68o   (The temp drops, so I will use a -16.68o in the calculation below)

Then the volume expansion formula is

V = VoT

V = (.00096)(.053004)(-16.68)

V = -8.5 X 10-4 m3

The new volume is therefore .053004 - (8.5 X 10-4) = .05216 m3

Converting that back to gallons.

(.05216)/(3.786 X 10-3) = 13.78 gallons

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