Question

Supposing a bridge is built from pieces of 4.46m long newly fabricated metal of linear expansivity 9.5×10^-6. If the gaps between the metals are 5.18mm on a day with temperature 15C, at what temperature will the pieces of metal begin to touch one another?

Answer 1

Solution. By definition of the temperature coefficient of linear expansion

$$\alpha = \frac {\Delta l}{l_0 \Delta t}$$

where α=9.5×10^-6 ⁰C^-1 is temperature coefficient of linear expansion; ∆l=5.18 m^-3; l₀ =4.46 m is particle length at initial temperature t₀=15⁰C; ∆t=(t-t₀) is temperature difference. Therefore, the final temperature is equal to

$$t=t_0+\frac{\Delta l}{l_0 \alpha}=15+\frac{5.18\times 10^{-3}}{4.46 \times 9.5\times 10^{-6}}\approx 137^0C$$

Answer.

$$t= 137^0C$$