Rail temperature expansion

How does the rail lengthen when the temperature changes from -30 °C to 30 °C if it is 25 m long at 0 °C? The temperature coefficient of longitudinal expansion is 12.10na-6Kna-1.

Final Answer:

Δ =  0.0181 m

Step-by-step explanation:

$$\begin{gathered} \alpha =12.10\cdot 10^{-6}\doteq 1.21\cdot 10^{-5}1\text{/K} \\ {l}_0=25\text{m} \\ {t}_0=0\text{°C} \\ {t}_1=-30\text{°C} \\ {t}_2=30\text{°C} \\ {l}_1=l_0\cdot (1+\alpha \cdot (t_1-t_0))=25\cdot (1+1.21\cdot 10^{-5}\cdot ((-30)-0))\doteq 24.9909\text{m} \\ {l}_2=l_0\cdot (1+\alpha \cdot (t_2-t_0))=25\cdot (1+1.21\cdot 10^{-5}\cdot (30-0))\doteq 25.0091\text{m} \\ \Delta =l_2-l_1=25.0091-24.9909=0.0181\text{m} \end{gathered}$$

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