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Q.
The volume of a metal sphere increases by $0.24\%$ when its temperature is raised by $40^{\circ}C$. The coefficient of linear expansion of the metal is
Thermal Properties of Matter
Solution:
From, $V_{T}=V_{0}\left(1+\gamma\Delta T\right)$
$\Rightarrow \frac{V_{T}-V_{0}}{V_{0}}=\gamma\Delta T$
$\frac{0.24}{100}=\gamma\,40\,{}^{\circ}C$
$\gamma=\frac{0.24}{100 \times 40}=6 \times 10^{-5}\,{}^{\circ}C^{-1}$
Coefficient of linear expansion,
$\alpha=\frac{\gamma}{3}=\frac{6\times10^{-5}}{3}$
$=2 \times 10^{-5}\,{}^{\circ}C^{-1}$