Answer to Question #1504 in Mechanics | Relativity for jon allen

Question

The density of gasoline is 730 kg/m3 at 0 degrees C. One gallon of gasoline occupies 0.0038 m^3.
Gasoline’s volume expansion coefficient is 0.00096 degrees C^−1. How many extra kilograms of gasoline are obtained when fifteen gallons of gasoline are bought at 0 degrees C rather than at 18 degrees C (temperature at the filling station)? Answer in units of kg.

Answer 1

The volume of fifteen gallons is
V(T=0) = 15 *0.0038 = 0.057 m³

The volume expansion of the gasoline while heating from 0C to 18C:
Δ V = V * α * ΔT = 0.0.057 * 0.00096 * (18-0) = 0.00098496 m³

The mass of gasoline in this extra volume would be
m = 0.00098496[m³] * 730 [kg/m³] = 0.719 kg