A 2.00-liter aluminum cylinder at 5.00°C is filled to the brim with gasoline at

Question

A 2.00-liter aluminum cylinder at 5.00°C is filled to the brim with gasoline at the same temperature. If the aluminum and gasoline are warmed to 55.0°C, how much gasoline spills out? [Hint: Be sure to account for the expansion of the container. Also, ignore the possibility of evaporation, and assume the volume coefficients are good to three digits.

__________________ cm3

Average Coefficients of Expansion for Some Materials Near Room Temperature Average Coefficient Average Coefficient of Volume Expansion of Linear Expansion Material Material [(OC) IOC) 1.12 X 10 Ethyl alcohol 24 X 10 Aluminum Brass and bronze 19 X 10-6 1.24 x 10 Benzene 17 x 10 1.5 X 10 Copper Acetone Glass ordinary 4.85 x 10-4 9 x 10 Glycerin 1.82 x 10 Glass (Pyrex®) 3.2 x 10 Mercury 29 X 10 9.0 X 10 Lead Turpentine 11 X 10 Steel Gasoline 9.6 X 10 3.67 x 10-3 Invar (NiFe alloy) 0.9 X 10 Air 12 X 10-6 8.665 X 10 Concrete Helium

Explanation / Answer

the change in the volume of gasoline

deltaV/V0 = 9.6 x10^-4

deltaV = 9.6x10^-4*2000 ml = 1.92 ml

the change in the volume of container

deltaV/V0 = 2.4 x10^-5

deltaV = 2.4 x10^-5 *2000 = 4.8 x10^-2 ml = 0.048 ml

the amount of spill

1.92 - 0.048 = 1.872 ml

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