An automobile gas tank is filled to its capacity of 15.00 gallons with the gasoline at an initial temperature of 10 $\degree$C.The automobile is parked in the sun causing the gasoline's temperature to rise to 60 $\degree$C.If the coefficient of volume expansion for gasoline is 9.6 x 10^-4/C $\degree$,what volume runs out the overflow tube? Assume the change in volume of the tank is negligible.

Question

Quizplus · Accepted Answer

The volume of gasoline that runs out of the overflow tube can be calculated using the formula:

ΔV = βVinitialΔT

where ΔV is the change in volume, β is the coefficient of volume expansion, Vinitial is the initial volume of gasoline, and ΔT is the change in temperature.

We can first convert the temperatures to Celsius:

Initial temperature = (10°F - 32) × 5/9 = -12.22°C
Final temperature = (60°F - 32) × 5/9 = 15.56°C

Using the given values, we can calculate:

ΔV = (9.6 × 10^-4 1/°C) x (15.00 gallons) x (15.56°C - (-12.22°C))

ΔV = 0.71952 gallons

Rounding to two significant figures, the volume that runs out the overflow tube is 0.72 gallons, which is choice (C).

An Automobile Gas Tank Is Filled to Its Capacity of 15.00