Question

The density of gasoline is 730 kg/m3 at 0C.
How many extra kilograms of gasoline are
obtained when thirteen gallons of gasoline are
bought at 0C rather than at 25C (tempera-
ture at the filling station)? One gallon of gaso-
line occupies 0.0038 m3 and gasoline’s volume
expansion coefficient is 0.00096(C)−1.
Answer in units of kg

Answer 1

The density of gasoline is 730 kg/m³ at 0C. How many extra kilograms of gasoline are obtained when thirteen gallons of gasoline are bought at 0 C rather than at 25 C (temperature at the filling station)? One gallon of gasoline occupies 0.0038 m³ and gasoline's volume expansion coefficient is 0.00096 (C)⁻¹. Answer in units of kg

Solution:

Let:

$$\rho = 730 \, \text{Kg/m}^3$$ $$T_1 = 0{}^\circ \text{C}$$ $$T_2 = 25{}^\circ \text{C}$$ $$V = 30 \, \text{gallons} = 30 \times 0.0038 = 0.114 \, \text{m}^3$$ $$\alpha = 0.00096 \, {}^\circ\text{C}^{-1}$$ $$m - ?$$ $$m = \rho \Delta V, \text{ were } \Delta V = \alpha V (T_2 - T_1)$$ $$m = \rho \alpha V (T_2 - T_1) = 730 \times 0.00096 \times 0.114 \times (25 - 0) = 2 \, \text{Kg} \, (1.99728)$$

Answer: 2 Kg