Question

On a cold morning (35 ∘F , or 1.7 ∘C ) you fill the gas tank in your car so that it is completely full with 14 gallons of gasoline. Later that day, when the temperature is 70 ∘F (21 ∘C ), you notice that a small volume of gasoline has leaked out of the tank. How much was lost due to the thermal expansion of the gasoline? The coefficient of volume expansion for gasoline is 9.6×10−4(∘C−1) . You can assume that the thermal expansion of the tank is negligible. 0.47 gallons 0.26 gallons 0.28 gallons 0.018 gallons

Answer 1

Approximately 0.47 gallons of gasoline is lost due to thermal expansion.

Step-by-step explanation:

The amount of gasoline lost due to thermal expansion can be calculated using the equation for volume expansion. We can assume that the thermal expansion of the tank is negligible, so we only need to calculate the change in volume of the gasoline. The coefficient of volume expansion for gasoline is 9.6×10-4 (°C-1).

To calculate the change in volume, we can use the equation:

ΔV = βVΔT

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

Given that the initial volume V is 14 gallons and the change in temperature is 21 °C - 1.7 °C = 19.3 °C:

ΔV = (9.6×10-4 °C-1) (14 gallons) (19.3 °C)

ΔV ≈ 0.47 gallons

Therefore, approximately 0.47 gallons of gasoline is lost due to thermal expansion.