Answer
a.
the aluminum cube
b.
$2.5\times 10^{-5}\mathrm{m}^{3}$
Work Step by Step
a.
The volume expansion coefficient $\beta$ is three times the linear coefficient $\alpha$, which we find in table 16-1.
Since aluminum has the greater $\alpha$, it also has the greater $\beta$, so
$\Delta V=\beta V\Delta T \qquad$ 16-6
will be greater for the aluminum cube.
b.
$\beta=3\alpha$
$\Delta V_{\mathrm{A}1}-\Delta V_{\mathrm{C}\mathrm{u}}=3\alpha_{\mathrm{A}1}V_{0}\Delta T-3\alpha_{\mathrm{C}\mathrm{u}}V_{0}\Delta T$
$=3(\alpha_{\mathrm{A}1}-\alpha_{\mathrm{C}\mathrm{u}})V_{0}\Delta T$
$=3[(24-17)\times 10^{-6}(\mathrm{C}^{\mathrm{o}})^{-1}](0.016\mathrm{m}^{3})(97-23)^{\mathrm{o}}\mathrm{C}$
$=2.5\times 10^{-5}\mathrm{m}^{3}$
