An automobile gas tank is filled to its capacity of 20.00 gallons with the gasoline at an initial temperature of 10°C.The automobile is parked in the Sun causing the gasoline's temperature to rise to 60°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. A) 1.74 gallons B) 0.96 gallon C) 0.72 gallon D) 0.30 gallon

Question

Quizplus · Accepted Answer

First, we need to find the expansion of gasoline due to the change in temperature. Using the formula for volume expansion, we have:

ΔV = VαΔT

where ΔV is the change in volume, V is the initial volume (20.00 gallons), α is the coefficient of volume expansion for gasoline (9.6 × 10^-4 /°C), and ΔT is the change in temperature (60°C - 10°C = 50°C).

Plugging in the values, we get:

ΔV = (20.00 gal) x (9.6 × 10^-4 /°C) x (50°C) = 0.96 gal

This means that the gasoline expands by 0.96 gallons as it heats up. Since the tank is already full, the excess gasoline will flow out the overflow tube. Therefore, the volume that runs out the overflow tube is 0.96 gallons.

The best choice is B, 0.96 gallon.

An Automobile Gas Tank Is Filled to Its Capacity of 20.00