Question

Length of a wire at room temperature is 4.55 m, when the temperature increases upto $100$ then its length becomes 4.57m. The coefficient of linear expansion $\left(\alpha \right)$ of the given wire is:

• A. $5.021\times {10}^{-5}{K}^{-1}$
• B. $6.021\times {10}^{-5}{K}^{-1}$
• C. $7.021\times {10}^{-5}{K}^{-1}$
• D. $8.021\times {10}^{-5}{K}^{-1}$

Answer 1

The correct option is B $6.021\times {10}^{-5}{K}^{-1}$

Here, $T_1=27=273+27=300k$
$T_2=100=273+100=373k$
$L_1=4.55m,L_2=4.57m$
As, $L_2=L_1[1+\alpha (T_2-T_1)]$
$\therefore 4.57=4.55[1+\alpha \left(373-300\right)]$
$4.57=4.55[1+\alpha \times 73]$
or $\alpha =[\frac{4.57}{4.55}-1]\times \frac{1}{73}=\left[\frac{4.57-4.55}{4.55}\right]\times \frac{1}{73}$
$\alpha =6.021\times {10}^{-5}{K}^{-1}$