Question

A thin copper wire of length $L$ increases 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. $4$%

Answer 1

The correct option is B $2$%

Given$:$

$\Delta T=100-0=100°C$

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

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

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

$0.01=\alpha \times 100$

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

Given Area of copper plate $=2L\times L=2L^2$

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 $\left(B\right)$ is correct answer.