Question

A thin copper wire length L increases its length by 1% heated from temperature $T_1$ and $T_2$ What is the percentage change in area when a thin copper plate having dimension 2Lx L is heated from $T_1$ to $T_2$

• A. 0.5 %
• B. 1 %
• C. 2 %
• D. 4 %

Answer 1

The correct option is C 2 %

$\Delta T=100-0=100°C$

$\Delta L/L=length=L=1$

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

$\Delta L/L=\alpha x100$

$0.01=\alpha x100$

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

Given Area of copper plate $=2LxL=2L^2$

By thermal expansion theory$:$

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

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

but$,$

$\beta =2\alpha$

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

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

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

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

Hence,

option $\left(C\right)$ is correct answer.