# Chapter 13 - Problems - Page 497: 17

(a) The change in volume of the metallic dental filling is $-0.053~mm^3$ (b) The change in volume of the cavity is $-0.021~mm^3$

#### Work Step by Step

(a) We can find the change in volume due to the decrease in temperature: $\Delta V = \beta~\Delta T~V$ $\Delta V = (42\times 10^{-6}~K^{-1})(-42~K)(30~mm^3)$ $\Delta V = -0.053~mm^3$ The change in volume of the metallic dental filling is $-0.053~mm^3$ (b) We can find the change in volume due to the decrease in temperature: $\Delta V = \beta~\Delta T~V$ $\Delta V = (17\times 10^{-6}~K^{-1})(-42~K)(30~mm^3)$ $\Delta V = -0.021~mm^3$ The change in volume of the cavity is $-0.021~mm^3$

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