A fuel tank contains 330,000 gallons of #4 fuel oil at 80°F. How many gallons would it read if the temperature was raised to 95°F? Coefficient of expansion is .000345

A fuel tank contains 330,000 gallons of #4 fuel oil at 80°F. How many gallons would it read if the temperature was raised to 95°F? Coefficient of expansion is .000345

• A. 331,708
• B. 332,000
• C. 330,400
• D. 331,000

Answer: (A)

When liquids warm, they expand in volume. The amount of expansion can be estimated with V = V0(1 + βΔT), where β is the volumetric expansion coefficient and ΔT is the temperature change. Here, V0 = 330,000 gallons, β = 0.000345 per °F, and ΔT = 95 − 80 = 15°F. Multiply β by ΔT: 0.000345 × 15 = 0.005175. So V = 330,000 × (1 + 0.005175) = 330,000 × 1.005175 = 331,707.75 gallons. Rounded to the nearest gallon, the read would be 331,708 gallons.

When liquids warm, they expand in volume. The amount of expansion can be estimated with V = V0(1 + βΔT), where β is the volumetric expansion coefficient and ΔT is the temperature change.

Here, V0 = 330,000 gallons, β = 0.000345 per °F, and ΔT = 95 − 80 = 15°F. Multiply β by ΔT: 0.000345 × 15 = 0.005175. So V = 330,000 × (1 + 0.005175) = 330,000 × 1.005175 = 331,707.75 gallons. Rounded to the nearest gallon, the read would be 331,708 gallons.