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, of olive oil spill over the top of the beaker.What is the coefficient of linear expansion of the glass?

Question

Quizplus · Accepted Answer

The volume of the olive oil that spills over the top of the beaker is given by:
ΔV = βVΔT
where β is the coefficient of volume expansion, V is the initial volume of the olive oil and ΔT is the change in temperature.
Substituting the given values, we get:
ΔV = (0.68 × 10^-3 K^-1) (1.00 L) (25 C°) = 0.017 L
Therefore, 0.017 L of olive oil spills over the top of the beaker.
Since the beaker is filled to the brim, the spilled olive oil has the same volume as the increase in volume of the glass beaker due to its expansion. Let's call this volume Vg.
ΔVg = ΔV = 0.017 L
The change in volume of the glass beaker is given by:
ΔVg = VgβgΔT
where βg is the coefficient of linear expansion of the glass.
The initial volume of the glass beaker is also 1.00 L, since it is filled to the brim with olive oil.
Substituting the given and calculated values, we get:
0.017 L = (1.00 L) βg (25 C°)
Solving for βg, we get:
βg = 4.0 × 10^-6 K^-1
Therefore, the coefficient of linear expansion of the glass is 4.0 × 10^-6 K^-1, which corresponds to choice B.

The Coefficient of Volume Expansion of Olive Oil Is 0