How much has the volume of the gasoline decreased when it is unloaded in New York.?

Question

A tanker ship is filled with 2.25 x 10^5 m^3 of gasoline at a refinery in southern Texas when the temperature is 17.2 degrees C. When the ship arrives in New York City, the temperature is 1.3 degrees C. The coefficient of volumetric expansion for gasoline is 9.50 x 10^-4/C degrees.

Answer 1

Just like compound interest, thermal expansion depends on the computation interval. If you start from a new initial volume V0 for each of a series of smaller intervals (say 1 degree C) you'll get a different answer than if you calculate the whole 15.9 C temperature change for one V0. Where precision counts (and where we assume a truly constant expansion rate over the whole temperature range) the equation is:
V = V0 * (1 - 0.00095) ^ 15.9
V = 2.25E5 * 0.985001... = 221625.32 m^3, a decrease of 3374.68 m^3.

Answer 2

Use the formula
V = V°(1-γΔT)

Here, V° = the volume at Texas = 2.25*10^5 m3
V = Volume in NY
γ = The coefficient of expansion = 9.5*10^-4
ΔT = Change in the temperature = 17.2-1.3 = 15.9°C

So, the decrease in volume = V°-V
= V°γΔT
= 2.25*10^5*9.5*10^-4*15.9
=3398.625 m^3