An automobile gas tank is filled to its capacity of 19 gallons with the gasoline at an initial temperature of 14°C.The automobile is parked in the sun causing the gasoline's temperature to rise to 56°C.If the coefficient of volume expansion for gasoline is 9.6 × 10−⁴/C°,what volume runs out the overflow tube? Assume the change in volume of the tank is negligible.

Question

Quizplus · Accepted Answer

The change in volume of the gasoline due to the increase in temperature can be calculated using the following equation:

ΔV = VαΔT

Where:
ΔV = change in volume
V = initial volume
α = coefficient of volume expansion
ΔT = change in temperature

Substituting the given values:
V = 19 gallons
α = 9.6 × 10−5 1/C°
ΔT = 56°C - 14°C = 42°C

ΔV = (19 gallons) × (9.6 × 10−5 1/C°) × (42°C) = 0.077 gallons

Therefore, the volume that runs out of the overflow tube is approximately 0.077 gallons, which is closest to choice C (0.77 gallons).

An Automobile Gas Tank Is Filled to Its Capacity of 19