Question

A car has a 69 Liter steel gas tank filled to the top with gasoline when the temperature is 3oC. The coefficient of volume expansion of gasoline is β = 9.00×10-4K^-1. Taking the expansion of the steel tank into account, how much gasoline spills out of the tank when the car is parked in the sun and its temperature rises to 19oC?

Answer 1

Let the volume of gasoline is Vt at 19*C, than
=>Vt = V{1+(β x delta t)}
=>Vt = 69[1+{0.900 x 10^-3 x (19-3)}]
=>Vt = 69[1+{0.900 x 10^-3 x 16}]
=>Vt = 69[1+0.0144]
=>Vt = 69 x 1.0144 = 69.6636 L
Let the coefficient of steel linear expansion is 11 x 10^6; Thus β for steel = 3 x 11 x 10^-6
=>β for steel = 33 x 10^-6
Let the volume of steel at 19*C is Vt,
=>Vt = V{1+(β x delta t)}
=>Vt = 69[1+{33 x 10^-6 x (19-3)}]
=>Vt = 69[1+{33 x 10^-6 x 16}]
=>Vt = 69 x 1.000528 = 69.0367 L
Thus the spill over volume = 69.6636 - 69.0367 = 0.9569 L