A. Early in the morning, when the temperature is 6.0 C, gasoline is pumped into

Question

A. Early in the morning, when the temperature is 6.0 C, gasoline is pumped into a car's 51-L steel gas tank until it is filled to the top. Later in the day the temperature rises to 26 C. Since the volume of gasoline increases more for a given temperature increase than the volume of the steel tank, gasoline will spill out of the tank.

How much gasoline spills out in this case?

Express your answer using two significant figures.

B. Longest Suspension Bridge The world's longest suspension bridge is the Akashi Kaikyo Bridge in Japan. The bridge is 3910m long and is constructed of steel. How much longer is the bridge on a warm summer day (30.0C) than on a cold winter day (5.00C)?

Explanation / Answer

You can use the volumetric expansion rate for both gas and steel.

.gas = 950 x 10^-6 /K

.steel = 36 x 10^-6 /K

Volumetric expansion of steel tank
V = V * T *
V = 51l * (20C) * 36 x 10^-6 /K
V =037 l

Volumetric expansion of gas
V = V * T *
V = 51l * (20C) * 950 x 10^-6 /K

V = .969 l

Amount spilled = .969 l - .037 l = .932 l

b).For linear thermal expansion, we have

Lt = L0( 1 + alpha * T)

where

Lt = Final length
L0 = Initial Length
T= (Final Temp. - Initial Temp.) and
alpha = Coefficient of linear expansion of metal (steel in your case = 17.3 X 10 ^ -6/Celsius

Here, it has been assumed that the bridge is a homogeneous object made up of pure steel.

Here, T =30-(-5)=35 c

L0=3910 m

Lt=3912.367 m

elongation=2.7635 m

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