An automobile fuel tank is filled to the brim with 45.3 liters (12.1 gallon) of gasoline at 14.5 degrees C. Immediately afterward, the vehicle is parked in the Sun, where the temperature is 34.5 degrees C. How much gasoline (in Liter) overflows from the tank as a result of the expansion? (Neglect the expansion of the tank).

β = ΔV/V•ΔT

β =10•10⁻⁴(1/℃)
ΔV=β•V•ΔT=10•10⁻⁴43.3•10⁻³•(34.5-14.5)=8.66•10⁻⁴ m³=0.866 liter.

Answer

To determine the amount of gasoline that overflows from the tank as a result of expansion, we need to calculate the change in volume due to the increase in temperature.

The coefficient of volume expansion for gasoline is approximately 0.00095 per degree Celsius.

First, we need to calculate the change in temperature:
ΔT = T2 - T1
ΔT = 34.5°C - 14.5°C
ΔT = 20°C

Next, we'll calculate the change in volume:
ΔV = V0 * β * ΔT
where V0 is the initial volume, β is the volume expansion coefficient, and ΔT is the change in temperature.

Converting the initial volume to liters:
V0 = 12.1 gallons * 3.78541 liters/gallon
V0 = 45.8749 liters

Now we can calculate ΔV:
ΔV = 45.8749 liters * 0.00095/°C * 20°C
ΔV = 0.087160775 liters

Therefore, approximately 0.087 liters of gasoline overflows from the tank as a result of the expansion.

To find out how much gasoline overflows from the tank as a result of expansion, we need to calculate the change in volume of gasoline due to the change in temperature. Here are the steps to do so:

1. Convert the initial fuel volume from gallons to liters:
- 1 gallon = 3.78541 liters
- Initial fuel volume = 12.1 gallons * 3.78541 liters/gallon

2. Use the formula for volume expansion:
ΔV = V₀ * β * ΔT

Where:
- ΔV is the change in volume
- V₀ is the initial volume
- β is the coefficient of volume expansion of the substance
- ΔT is the change in temperature

3. Find the coefficient of volume expansion of gasoline.
The coefficient of volume expansion of gasoline is 0.00096 per degree Celsius.

4. Calculate the change in temperature:
ΔT = Final temperature - Initial temperature

ΔT = 34.5 degrees Celsius - 14.5 degrees Celsius

5. Calculate the change in volume:
ΔV = V₀ * β * ΔT

6. Calculate the final volume of gasoline:
Final volume = Initial volume + ΔV

Let's perform the calculations step by step:

Step 1:
Initial fuel volume = 12.1 gallons * 3.78541 liters/gallon
Initial fuel volume = 45.935741 liters (rounded to four decimal places)

Step 2:
ΔV = 45.935741 liters * 0.00096 per degree Celsius * ΔT

Step 3:
ΔT = 34.5 degrees Celsius - 14.5 degrees Celsius
ΔT = 20 degrees Celsius

Step 4:
ΔV = 45.935741 liters * 0.00096 per degree Celsius * 20 degrees Celsius

Step 5:
ΔV ≈ 0.087792 liters (rounded to six decimal places)

Step 6:
Final volume = 45.935741 liters + 0.087792 liters
Final volume ≈ 45.99 liters

Therefore, the gasoline overflows from the tank as a result of expansion by approximately 0.09 liters (rounded to two decimal places).