Question

A container made of steel, which has a coefficient of linear expansion 11 ✕ 10−6 (°C)−1, has a volume of 55.0 gallons. The container is filled to the top with turpentine, which has a coefficient of volume expansion of 9.0 ✕ 10−4 (°C)−1, when the temperature is 10.0°C. If the temperature rises to 25.5°C, how much turpentine (in gal) will spill over the edge of the container?

Answer 1

Answer:

a. ΔV = 0.48895 gal

b. ΔV = 1.246 gal

Explanation:

V₀ = 55.0 gal

β₁ = 11 x 10 ⁻⁶ (° C) ⁻¹

β₂ = 9.0 x 10 ⁻⁴ (° C) ⁻¹

a.

ΔT = 10.0 ° C

ΔV = (β₁ - β₂) * V₀ * ΔT

ΔV = [ 9.0 x 10 ⁻⁴ (° C) ⁻¹ - 11 x 10 ⁻⁶ (° C) ⁻¹ ] * 55.0 gal * 10 ° C

ΔV = 0.48895 gal

b.

ΔT = 25.5 ° C

ΔV = (β₁ - β₂) * V₀ * ΔT

ΔV = [ 9.0 x 10 ⁻⁴ (° C) ⁻¹ - 11 x 10 ⁻⁶ (° C) ⁻¹ ] * 55.0 gal * 25.5 ° C

ΔV = 1.246 gal