Question

Length of a wire at room temperature is $4.55m$, when the temperature increase upto ${100}^{o}C$ 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 $6.021\times {10}^{-5}{K}^{-1}$

Given: The initial temperature of wire, $T_1={27}^{o}C=273+27=300K$

The final temperature of the wire is $T_2={100}^{o}C=273+100=373K$
Initial length of the wire, $L_1=4.55m,L_2=4.57m$

The new length of the wire is given by:

$L_2=L_1[1+\alpha (T_2-T_1\left)\right]$

$\therefore 4.57=4.55[1+\alpha (373-300\left)\right]$

$4.57=4.55[1+\alpha \times 73$

or $\alpha =[\frac{4.57}{4.55}-1]\times \frac{1}{73}=\left[\frac{4.57-4.55}{4.55}\right]\times \frac{1}{73}$

$\alpha =6.021\times {10}^{-5}{K}^{-1}$