A 15.0-gal container is filled with gasoline. Neglect the change in volume of the container and find how many gallons are lost if the temperature increases by 31.9°F. The volume expansion coefficient of gasoline is 9.60·10-4°C-1
To find out how many gallons are lost if the temperature increases, we need to calculate the change in volume of the gasoline.
The volume expansion coefficient provides us with information about how the volume changes with temperature. In this case, it is given as 9.60·10-4°C-1. However, we need to convert the change in temperature to degrees Celsius since the coefficient is given in terms of Celsius.
To convert the change in temperature from Fahrenheit (°F) to Celsius (°C), we use the formula:
ΔT(°C) = (ΔT(°F) - 32) × (5/9)
Let's calculate the change in temperature:
ΔT(°C) = (31.9°F - 32) × (5/9)
= -0.11°C
Now that we have the change in temperature in degrees Celsius, we can calculate the change in volume of the gasoline using the volume expansion coefficient:
ΔV/V = β * ΔT
Where:
ΔV/V is the fractional change in volume
β is the volume expansion coefficient
ΔT is the change in temperature
Let's calculate the fractional change in volume:
ΔV/V = (9.60·10-4°C-1) * (-0.11°C)
= -1.056·10-4
To find the actual change in volume of the gasoline, we multiply the fractional change by the initial volume:
ΔV = (-1.056·10-4) * (15.0 gal)
= -1.584·10-3 gal
Therefore, the gasoline loses approximately 0.001584 gallons when the temperature increases by 31.9°F.