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## Homework Statement

The coefficient of volume expansion of olive oil is 0.68 × 10-3 K-1. A 1-liter 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 liters of olive oil spill

over the top of the beaker. What is the coefficient of linear expansion of glass?

## Homework Equations

ΔV = βV

_{i}ΔT

ΔV = (3α)V

_{i}ΔT

β = Coefficient of Volume Expansion

α = Coefficient of Linear Expansion

## The Attempt at a Solution

V

_{i}= 1.0 L (for both olive oil and the beaker)

T

_{i}= 20°C = 293.15 K

ΔT = 25°C = 298.15 K

V

_{lost}= 0.0167 L

β

_{olive}= 0.68x10

^{-3}K

^{-1}

α

_{glass}= ?

__Calculate volume expansion of beaker__ΔV

_{olive}= (0.68x10

^{-3}K

^{-1}) * (1.0 L) * (298.15 K)

= 0.202742 L

ΔV

_{glass}= ΔV

_{olive}- V

_{lost}

= 0.202742 L - 0.0167 L

= 0.186042 L (Volume increase for glass beaker)

__Calculate Coefficient of Linear Expansion for Glass Beaker__0.186042 L = (3α

_{glass})(1.0 L)(298.15 K)

0.186042 L = 894.45 L⋅K * α

_{glass}

α

_{glass}= 0.186042 L / (894.45 L⋅K)

= 0.000208 / K =

**2.1x10**

^{-4}K^{-1}This is

*very*close to one of the actually answers (there are 5). One of them is 2x10

^{-5}K

^{-1}. The teacher has said that he has removed the correct answer for some of the questions, and that we are to explain why are answer is correct if that is the case. Is my answer correct? If not, what did I do wrong?