Question

The density of gasoline is 7.30 ? 10² kg/m³ at 0°C. Its average coefficient of volume expansion is 9.60 ? 10^?4 (°C)^?1, and note that

1.00 gal = 0.00380 m³.

(a) Calculate the mass of 11.3 gal of gas at 0°C. (Give your answer to at least two decimal places.)
kg

(b) If 1.000 m³ of gasoline at 0°C is warmed by 19.5°C, calculate its new volume. (Give your answer to at least two decimal places.)
m³

(c) Using the answer to part (b), calculate the density of gasoline at 19.5°C. (Give your answer to at least three significant figures.)
kg/m³

(d) Calculate the mass of 11.3 gal of gas at 19.5°C. (Give your answer to at least two decimal places.)
kg

(e) How many extra kilograms of gasoline would you get if you bought 11.3 gal of gasoline at 0°C rather than at 19.5°C from a pump that is not temperature compensated?
kg

Answer 1

a)
1 gal of gas = 0.0038 m³.
11.3 gal = 11.3 x 0.0038 = 0.04294 m³.

Mass = volume x density
= 0.04294 x 7.3 x 10²
= 31.35 kg

b)
V(T) = Vo [1 + T]
Where V(T) is the volume at temperature T and Vo is the initial volume.
V(T) = 1 x [1 + 9.6 x 10^-4 x (19.5 - 0)]
= 1.01872 m³.

c)
Initial density = 7.3 x 10² kg/m³.
ie, 7.3 x 10² kg gas occupied 1 m³ volume.
At 19.5 degrees, volume expand from 1 m³ to 1.01872 m³
New density = (7.3 x 10²) / 1.01872
= 7.17 x 10² kg/m³.

d)
Density at 19.5 degrees = 7.17 x 10² kg/m³.
11.3 gal = 11.3 x 0.0038 = 0.04294 m³.

Mass = volume x density
= 0.04294 x 7.17 x 10²
= 30.77 kg

e)
Extra mass = 31.35 - 30.77
= 0.576 kg