Answer:
43.7 °C
Explanation:
[tex]\alpha_b[/tex] = Coefficient of linear expansion of brass = [tex]18\times 10^{-6}\ ^{\circ}C[/tex]
[tex]\alpha_s[/tex] = Coefficient of linear expansion of steel = [tex]11\times 10^{-6}\ ^{\circ}C[/tex]
[tex]L_{0b}[/tex] = Initial length of brass = 31 cm
[tex]L_{0s}[/tex] = Initial length of steel = 11 m
[tex]\Delta L[/tex] = Total change in length = 3 mm
Total change in length would be
[tex]\Delta L=\Delta L_b+\Delta L_s\\\Rightarrow \Delta L=L_{0b}\alpha_b\Delta T+L_{0s}\alpha_b\Delta T\\\Rightarrow \Delta T=\frac{\Delta L}{L_{0b}\alpha_b+L_{0s}\alpha_b}\\\Rightarrow \Delta T=\frac{0.003}{0.31\times 18\times 10^{-6}+11\times 10^{-6}\times 11}\\\Rightarrow \Delta T=23.7\ ^{\circ}C[/tex]
[tex]\Delta T=23.7\\\Rightarrow T_f-T_i=23.7\\\Rightarrow T_f=23.7+T_i\\\Rightarrow T_f=23.7+20\\\Rightarrow T_f=43.7\ ^{\circ}C[/tex]
The final temperature is 43.7 °C
