Question

What is the percentage change in length of $1m$ iron rod if its temperature changes by ${100}^{\circ }C$? [$\alpha$ for iron is $2\times {10}^{-5}m{/}^{\circ }C$]

• A. $2\%$.
• B. $0.2\%$.
• C. $0.02\%$.
• D. $0.1\%$.

Answer 1

The correct option is B $0.2\%$.

Coefficient of thermal expansion is $\alpha =2\times {10}^{-5}/{}^{o}C$

Change in temperature is $\Delta \theta ={100}^{o}C$

Percentage change in length due to temperature change
$=\frac{\Delta \ell }{\ell }\times 100=\alpha \Delta \theta \times 100$
$=2\times {10}^{-5}\times 100\times 100$
$=0.2\%$