Thermal expansion: The coefficient of volume expansion of olive oil is 0.68 × 10^-3K^-1. A 1.00-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 spill over the top of the beaker. What is the coefficient of linear expansion of the glass? A) 1.0 × 10^-6K^-1 B) 4.0 × 10^-6K^-1 C) 1.0 × 10^-5K^-1 D) 2.0 × 10^-5K^-1 E) 3.0 × 10^-5K^-1

Question

Quizplus · Accepted Answer

The coefficient of linear expansion ($\alpha$) of the glass can be found by understanding that the volume expansion of the oil minus the volume expansion of the glass gives the overflowed oil volume. Given the coefficient of volume expansion of olive oil ($\beta_{oil}$) is $0.68 \times 10^{-3} K^{-1}$, and the volume of spilled oil is $0.0167 L$, we can calculate the volume expansion of the glass beaker to find its coefficient of linear expansion. Since the volume expansion coefficient ($\beta$) is approximately three times the linear expansion coefficient ($\alpha$), and knowing that the volume expansion of the beaker must be less than that of the oil for it to overflow, we can deduce that the correct coefficient of linear expansion for the glass that matches the given conditions is $4.0 \times 10^{-6} K^{-1}$. This value indicates a smaller expansion of the beaker compared to the oil, leading to the observed overflow.

Thermal Expansion: the Coefficient of Volume Expansion of Olive Oil