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  4. A metal cube of length 10.0 mm at 0° C (273 K ) is heated to 200° C (473 K ). Given: its coefficient of linear expansion is 2 × 10-5 K -1. The percent change of its volume is

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Q. A metal cube of length 10.0 mm at $0^{\circ} C (273 K )$ is heated to $200^{\circ} C (473 K )$. Given: its coefficient of linear expansion is $2 \times 10^{-5} K ^{-1}$. The percent change of its volume is

Thermal Properties of Matter

Solution:

$\frac{\Delta V}{V}=\gamma \cdot \Delta T=3 \alpha \Delta T=3\left(2 \times 10^{-5} K ^{-1}\right)(200 K )$
$=12 \times 10^{-3} \frac{\Delta V}{V}= 12 \times 10^{-3} \times 100 \%=1.2 \%$