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?

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Quizplus · Accepted Answer

The coefficient of volume expansion for the olive oil is given as $0.68 \times 10^{-3} \, \text{K}^{-1}$. The volume expansion of the oil can be calculated using the formula $\Delta V = \beta V_0 \Delta T$, where $\Delta V$ is the change in volume, $\beta$ is the coefficient of volume expansion, $V_0$ is the initial volume, and $\Delta T$ is the change in temperature. Given that $0.0167 \, \text{L}$ of oil spilled over, this is the volume expansion of the oil. The glass beaker also expands, but less oil would have spilled if the beaker did not expand. To find the coefficient of linear expansion ($\alpha$) of the glass, we use the relationship $\beta = 3\alpha$ for solids. By calculating the effective volume expansion of the oil that takes into account the expansion of the glass and solving for $\alpha$, we find that the coefficient of linear expansion for the glass matches the value given in option B, $4.0 \times 10^{-6} \, \text{K}^{-1}$.

The Coefficient of Volume Expansion of Olive Oil Is 0