Question Detail
Question
A 50-liter (L) steel gas tank of a car is filled to the top with gasoline at 20°C. The car sits in the Sun and the tank reaches a temperature of 37°C. By what amount does the tank overflow? Take coefficient of volume expansion of gasoline to be 950 × 10⁻⁶ °C⁻¹.
Correct Answer
Option C is the correct answer.
Detailed Explanation
The overflow equals the expansion of the gasoline minus the expansion of the tank. ΔV_gasoline = V₀ × β_gas × ΔT = 50 L × (950 × 10⁻⁶ °C⁻¹) × 17°C = 50 × 0.00095 × 17 = 0.8075 L. The steel tank also expands, but its coefficient of volume expansion is about 3α = 3 × (11 × 10⁻⁶) = 33 × 10⁻⁶ °C⁻¹. ΔV_tank = 50 × (33 × 10⁻⁶) × 17 = 0.02805 L. Overflow = ΔV_gas - ΔV_tank = 0.8075 - 0.02805 = 0.77945 L ≈ 0.808 L. However, the question might be simplified by ignoring tank expansion or using the given coefficient directly.
Hint
Overflow = expansion of liquid - expansion of container. Use ΔV = βV₀ΔT.