If volume of a block of metal changes by 0.12% when it is heated thrugh 20,^oC , coefficient of line

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10-1.Thermometry, Thermal Expansion and Calorimetry

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If the volume of a block of metal changes by $0.12\%$ when it is heated thrugh $20\,^oC$, the coefficient of linear expansion (in $^o{C^{ - 1}}$) of the metal is

A

$10^{-5}$

B

$2 \times {10^{ - 5}}$

C

$3 \times {10^{ - 5}}$

D

$5 \times {10^{ - 5}}$

Solution

The co-efficient of cubical expansion $y$ of the metal is given by

$Y=\frac{1}{V} \times \frac{\Delta V}{\Delta T}$

$Y=\frac{\Delta V}{V} \times \frac{1}{\Delta T}$

Here, $\frac{\Delta V}{V}=\frac{0.12}{100}$

$\Delta T=20^{\circ} \mathrm{C}$

$Y=\frac{0.12}{100} \times \frac{1}{20}$

$Y=6 \times\left.10^{-5}\right|^{0} C$

$\therefore$ Co-efficient of linear expansion of the metal is $:-$

$\alpha=\frac{Y}{3}=\frac{6.0 \times 10^{-5}}{3}$

$\alpha=2.0 \times\left.10^{-5}\right|^{0} C$

Standard 11

Physics

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