Question

Length of a wire at room temperature is $4.55\, m$, when the temperature increases upto $100^{\circ}C$ then its length becomes $4.57 \,m$. The coefficient of linear expansion $(\alpha)$ 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

Answer: (B)

Here, $T_{1}=27^{\circ}C=273+27=300\,K$
$T_{2}=100^{\circ}C=273+100=373\,K$
$L_{1}=4.55\,m$, $L_{2}=4.57\,m$
As, $L_{2}=L_{1}\,\left[1+\alpha\left(T_{2}-T_{1}\right)\right]$
$\therefore 4.57=4.55\left[1+\alpha\left(373-300\right)\right]$
$4.57=4.55\left[1+\alpha \times 73\right]$
or $\alpha=\left[\frac{4.57}{4.55}-1\right]\times\frac{1}{73}=\left[\frac{4.57-4.55}{4.55}\right]\times\frac{1}{73}$
$\alpha=6.021 \times10^{-5}\,K^{-1}$