Question

Did I do this problem on lineral thermal expansion correctly? Information was left out of the problem, so I assumed the material to be steel, as iron was not listed in my book.

You are asked to lay a railroad track. Each piece of track is 30.0m long and the temperature in the region varies from -10^oF in the winter to to 95^oF in the summer. How close can you lay down the successive tracks without causing undue stresses in the track?

My work: -10^oF = -23.3^o C and 95^oF = 35^oC; $\alpha$ steel = 1.2x10^{-5 o}C

$\Delta L=\alpha L_{o}\Delta T$ = (1.2x10^{-5 o}C)(30.0m)(58^oC) answer = 0.021m

Also, would the numerical value for the coefficient of linear thermal expansion be the same if the temperature was measured in degrees farhenheit?

My answer would be no because 1^oF = 5/9 of 1^oC. Also, I played around with some values and I got very different answers for $\alpha$ when I used farhenheit. Is this correct?

Answer 1

Your answer is correct since u have considered coefficient of thermal expansion and the temperature difference both in celcius.

The thermal expansion in fahrenheit scale would have a different value, never the less the answer would remain the same as we again considering the temperature in fahrenheit scale resulting in the same answer