A thin copper wire of length L increase in length by 1% when heated from temperature T₁ to T₂ .

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10-1.Thermometry, Thermal Expansion and Calorimetry

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A thin copper wire of length $L$ increase in length by $1\%$ when heated from temperature $T_1$ to $T_2$. What is the percentage change in area when a thin copper plate having dimensions $2L\times L$ is heated from $T_1$ to $T_2$ ? ....... $\%$

A

$1$

B

$2$

C

$3$

D

$4$

Solution

$\Delta T=100-0=100^{\circ} \mathrm{C}$

$\Delta L / L=$ length $=L=1 \%=1 / 100=0.01$

$\Delta L=\alpha L \Delta T$

$\Delta L / L=\alpha x 100$

$0.01=\alpha x 100$

$\alpha=0.01 / 100=1 \times 10^{-4}$

Given Area of copper plate $=2 L x L=2 L^{2}$

By thermal expansion theory,

$\Delta A=\beta A \Delta T$

$\Delta A / A=\beta \Delta T$

but,

$\beta=2 \alpha$

$\Delta A / A=2 \alpha \Delta T$

$=2 \times 1 \times 10^{-4} \times 100$

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

$\Delta A / A \times 100=2 \times 10^{-2} \times 100=2 \%$

Standard 11

Physics

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