The coefficient of volume expansion of a certain olive oil is 0.68 × 10^-3 K^-1.A 1.0-L glass beaker is filled to the brim with olive oil at room temperature.The beaker is placed on a range and the temperature of the oil and beaker increases by 25°C.As a result,0.0167 L of olive oil spills over the top of the beaker.Which of the following values is closest to the coefficient of linear expansion of the glass from which the beaker is made? A)1 × 10^-6 K^-1 B)4 × 10^-6 K^-1 C)1 × 10^-5 K^-1 D)2 × 10^-5 K^-1 E)3 × 10^-5 K^-1

Question

Quizplus · Accepted Answer

We can use the formula ΔV = V0βΔT to find the change in volume of the olive oil.

ΔV = (1.0 L)(0.68 × 10^-3 K^-1)(25°C) = 0.017 L

This is slightly larger than the amount of oil that spilled over, but we can assume that some of the oil may have been lost due to splashing or other factors.

Since the oil expands as it is heated, the beaker must also expand. We can use the formula ΔL = αL0ΔT to find the change in length of the beaker, where α is the coefficient of linear expansion.

ΔL = (0.0167 L)/(1.0 cm × 1.0 cm × h) where h is the height of the oil in the beaker.

We can assume that the height of the oil in the beaker is approximately equal to the height of the beaker itself, so h ≈ 10 cm.

ΔL = (0.0167 L)/(1.0 cm × 1.0 cm × 10 cm)(25°C) = 6.68 × 10^-6 m

Finally, we can use the formula α = ΔL/L0ΔT to find the coefficient of linear expansion.

α = (6.68 × 10^-6 m)/(10 cm)(25°C) = 2.67 × 10^-6 K^-1

The closest answer choice is B, 4 × 10^-6 K^-1.

The Coefficient of Volume Expansion of a Certain Olive Oil