Question

Um cabo elétrico com temperatura de 20C tem comprimento de 2,5m. Se a temperatura subir para 42C, qual o comprimento final? Dado: alfa (letra grega)=17.10-6 (o -6 é elevado ao 10)

Answer 1

$\textrm{Dados do exerc\'icio:}\\\\ T_0=20\ºC\ \| \ T=42\ºC\\ \Delta T=T-T_0\ \to\ \Delta T=42-20=22\ºC\\\\ L_0=2,5\ m\\ \alpha=17.10^{-6}\ \ºC^{-1}\\\\ \mathrm{Calculando\ \Delta L:}\\\\ \Delta L=L_0.\alpha.\Delta T\ \to\ \Delta L=2,5.1,7.10^{-5}.2,2.10^1\\ \mathbf{\Delta L=9,35.10^{-4}\ m}\\\\ \textrm{Calculando L:}\\\\ \Delta L=L-L_0\ \to\ 9,35.10^{-4}=L-2,5\\ L=9,35.10^{-4}+2,5\ \to\ L=9,35.10^{-4}+25000.10^{-4}\\ L=25009,35.10^{-4}\ \to\ \mathbf{L=2,500935\ m}$