Answer: The coefficient of expansion for the wire [tex]0.000028 (^oC)^{-1}[/tex].
Explanation:
Original length of the wire = L= 410.0000 m
Initial temperature =[tex]T_1=0.0^oC[/tex]
Final Temperature = [tex]T_2=30.0^oC[/tex]
Increase in Length of the wire = [tex]\Delta L=0.3444 m[/tex]
[tex]\frac{\Delta L}{L}=\alpha _{L}\times \Delta T=\alpha _{L}\times (T_2-T_1)[/tex]
[tex]\alpha _L=\frac{\Delta L}{L\times (T_2-T_1)}=\frac{0.3444 m}{410.0000 m\times (30.0^oC-0.0^oC)}[/tex]
[tex]\alpha _L=0.000028 (^oC)^{-1}[/tex]
The coefficient of expansion for the wire [tex]0.000028 (^oC)^{-1}[/tex].
