Imagine you've finished this academic year and gone home to enjoy your summer vacation. During one of your days of relaxation and non-academic bliss, however, you realize you need to run a few errands. After stopping at the gas station where you fill the gas tank to its capacity of 70 liters with gasoline at 20° Celcius, you park the car in the parking lot of your favorite CD store. The hot sun causes the gas temperature to rise to a toasty 137° Fahrenheit. What volume of gas runs out of the overflow tube? The volume expansion coefficient for gasoline is 950*10-6 C-1. You may ignore the thermal expansion of the tank and the small amount of gas consumed from the gas station to the CD store.
Volume = ?? in liters
HELP: Volume increases linearly with temperature.
HELP: You're looking for the change in volume. ΔV = V (initial)*β*ΔT.
since you are doing delta V over V it does not matter if you are using cubic meters or liters or whatever. Use liters
C = (5/9)(F-32)
C = (5/9)(137-32) = 58.3 deg C
delta T = 58.3 - 20 = 38.3
delts V / V = 950*10^-6 (38.3)
delta V = 70*950*10^-6 * 38.3
= 2.55 liters spilled on ground, like half a gallon
bad, bad :(
To calculate the volume of gas that runs out of the overflow tube, we can use the formula:
ΔV = V(initial) * β * ΔT
Where:
ΔV is the change in volume
V(initial) is the initial volume of the gas
β is the volume expansion coefficient for gasoline
ΔT is the change in temperature
According to the problem, the gas tank is filled to its capacity of 70 liters at 20° Celsius. The temperature then rises to 137° Fahrenheit.
To solve this problem, we need to convert the temperature from Fahrenheit to Celsius. To convert Fahrenheit to Celsius, we use the formula:
°C = (°F - 32) * 5/9
Using this formula, we can calculate the change in temperature:
ΔT = (137 - 32) * 5/9 - 20 = 57.2° Celsius
Next, we need to calculate the change in volume:
ΔV = 70 * (950 * 10^-6) * 57.2 = 0.038 liters
Therefore, the volume of gas that runs out of the overflow tube is approximately 0.038 liters.