Question

Suppose that the steel gas tank in your car is completely filled when the temperature is 16 °C. How many gallons will spill out of the 88-Liters tank when the temperature rises to 40 °C?

Answer 1

$ΔT = 40 -16 = 24 \; °C$

Change in volume of steel tank $= ΔV_x$

Change in volume of gasoline $= ΔV_g$

Coefficient of volume expansion of steel tank

$β_x = 30 \times 10^{-6} \; 1/°C$

Coefficient of volume expansion of gasoline

$β_g = 950 \times 10^{-6} \; 1/°C$

$V_0 = 88 \;L = 23.24 \;gal$

Change in volume of steel tank is

$ΔV_x = β_xV_0ΔT$

Change in volume of gasoline is

$ΔV_g = β_gV_0ΔT$

Required volume:

$ΔV = ΔV_g-ΔV_x \\ ΔV=(β_g -β_x)V_0ΔT \\ ΔV=(950 \times 10^{-6} -36 \times 10^{-6}) (23.24 \;gal) (24 \; °C) \\ ΔV= 0.509 \;gal$

Answer: 0.509 gal