# Chapter 13 - Problems - Page 497: 20

(a) The amount of water that spills over the top of the glass is $1.47~mL$ When the expansion of the glass is not considered, the amount of water that spills over the top of the glass is $1.69~mL$ (b) When the expansion of the glass is considered, the answer decreases by 13%

#### Work Step by Step

(a) We can find the change in volume of the glass due to the increase in temperature: $\Delta V = \beta~\Delta T~V$ $\Delta V = (27\times 10^{-6}~K^{-1})(30.0~K)(268.4~mL)$ $\Delta V = 0.217~mL$ We can find the change in volume of the water due to the increase in temperature: $\Delta V = \beta~\Delta T~V$ $\Delta V = (210\times 10^{-6}~K^{-1})(30.0~K)(268.4~mL)$ $\Delta V = 1.69~mL$ The amount of water that spills over the top of the glass is $1.69~mL-0.217~mL$ which is $1.47~mL$ When the expansion of the glass is not considered, the amount of water that spills over the top of the glass is $1.69~mL$ (b) We can find the fraction that the answer changed: $\frac{1.47~mL-1.69~mL}{1.69~mL} = -0.13$ When the expansion of the glass is considered, the answer decreases by 13%

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