p19_017.pdf

17. If V c is the original volume of the cup, α a is the coecient of linear expansion of aluminum, and ∆ T is

the temperature increase, then the change in the volume of the cup is ∆ V c =3 α a V c ∆ T . See Eq. 19–11.

If β is the coecient of volume expansion for glycerin then the change in the volume of glycerin is

∆ V g = βV c ∆ T . Note that the original volume of glycerin is the same as the original volume of the cup.

The volume of glycerin that spills is

∆ V g −

= 5 . 1

−

3 α a ) V c ∆ T

10 − 4 / C ◦

3 23

10 − 6 / C ◦ 100 cm 3 (6 C ◦ )

−

=0 . 26 cm 3

∆ V c = β