The coefficient of volume expansion of a certain olive oil is $0.68 \times 10 ^ { - 3 } \mathrm {~K}^{ - 1}$
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 $25 \mathrm { C } ^ { \circ }$ 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) $4 \times 10 ^ { - 6 } K ^ { - 1 }$
B) $1 \times 10 ^ { - 5 } K ^ { - 1 }$
C) $1 \times 10 ^ { - 6 } K ^{- 1}$
D) $2 \times 10 ^ { - 5 } \mathrm {~K} ^ { - 1 }$
E) $3 \times 10 ^ { - 5 } K ^{- 1}$

Question

The coefficient of volume expansion of a certain olive oil is $0.68 \times 10 ^ { - 3 } \mathrm {~K}^{ - 1}$
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 $25 \mathrm { C } ^ { \circ }$ 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) $4 \times 10 ^ { - 6 } K ^ { - 1 }$
B) $1 \times 10 ^ { - 5 } K ^ { - 1 }$
C) $1 \times 10 ^ { - 6 } K ^{- 1}$
D) $2 \times 10 ^ { - 5 } \mathrm {~K} ^ { - 1 }$
E) $3 \times 10 ^ { - 5 } K ^{- 1}$

Quizplus · Accepted Answer

The coefficient of linear expansion can be determined by understanding the relationship between the volume expansion of the oil and the volume expansion of the glass beaker. Given that 0.0167 L of oil spills over after a 25°C increase in temperature, we can calculate the volume expansion of the glass and compare it to the volume expansion of the oil to find the coefficient of linear expansion of the glass. The calculation involves using the formula for volume expansion ($\Delta V = \beta V_0 \Delta T$) and understanding that the volume expansion of the glass is less than that of the oil, which leads to the overflow. The coefficient of linear expansion for glass typically falls within the range of $10^{-6} K^{-1}$, making option A the most plausible choice based on the given data and the principles of thermal expansion.

The Coefficient of Volume Expansion of a Certain Olive Oil 0.68×10−3 K−10.68 \times 10 ^ { - 3 } \mathrm {~K}^{ - 1}0.68×10−3 K−1

The Coefficient of Volume Expansion of a Certain Olive Oil $0.68 \times 10 ^ { - 3 } \mathrm {~K}^{ - 1}$