Question

A piece of copper wire has a length of 2m at 10°C. Its length at 100°C is (co-efficient of linear

expansion of copper = 17 × 10^–6/°C).​

Answer 1

$\color{darkblue}\underline{\underline{\sf Given-}}$

• Lenght of copper wire $(\ell_1)$ = 2m at temperature $(\theta_1)$ = 10°C
• Temperature rise to $(\theta_2)$ = 100°C
• Coefficient of linear expansion ${\sf (\alpha)=17×10^{-6}/°C}$

$\color{darkblue}\underline{\underline{\sf To \: Find-}}$

• Final length after temperature rise $(\ell_2)$

$\color{darkblue}\underline{\underline{\sf Solution-}}$

$\Large\color{violet}\blacksquare\boxed{\sf \Delta \ell = \ell\alpha\Delta\theta}$

$\implies{\sf \ell_2-\ell_1=\ell_1\alpha(\theta_2-\theta_1)}$

$\implies{\sf \ell_2-2=2×17×10^{-6}×(100-90)}$

$\implies{\sf \ell_2-2=2×17×10^{-6}×10 }$

$\implies{\sf \ell_2-2=3060×10^{-6}}$

$\implies{\sf \ell_2-2=3.0×10^{-3}}$

$\implies{\sf \ell_2=3+2×10^{-3}}$

$\color{red}\implies{\sf \ell_2=5×10^{-3}m }$

$\color{darkblue}\underline{\underline{Answer-}}$

Final length after temperature rise $(\ell_2)$ is $\color{red}{\sf 5×10^{-3}m}$.