Answer:
[tex]T=283^{\circ}C[/tex]
Explanation:
Given a material with temperature coefficient of resistance c, the equation that relates the resistance [tex]R_0[/tex] at temperature [tex]T_0[/tex] and the resistance [tex]R[/tex] at temperature [tex]T[/tex] is
[tex]\frac{R-R_0}{R_0}=c(T-T_0)[/tex]
We want to double our resistance, so [tex]R=2R_0[/tex], thus having:
[tex]\frac{2R_0-R_0}{R_0}=\frac{R_0}{R_0}=1=c(T-T_0)[/tex]
For this T must be:
[tex]1=cT-cT_0[/tex]
[tex]T=\frac{1+cT_0}{c}[/tex]
which for our values means (with [tex]T=20^{\circ}C=293^{\circ}K[/tex], remember to write temperature in S.I., and that for silver [tex]c=0.0038^{\circ}K^{-1}[/tex]):
[tex]T=\frac{1+(0.0038^{\circ}K^{-1})(293^{\circ}K)}{(0.0038^{\circ}K^{-1})}=556^{\circ}K=283^{\circ}C[/tex]
