A steel railroad track has a length of 79 when the temperature is 2◦C. What is the increase in the length of the rail on a hot day when the temperature is 35◦C? The linear expansion coefficient of steel is 11 × 10−6 (◦C)−1.

We know that the length is 79 (there are no units of length in the question, so i will leave it as it is written, without units) when the temperature is 2°C.

We want to find the increase in length when the temperature is 35°C, knowing that the linear expansion coefficient is 11*10^(-6) °C^-1

The change in length is just given by the equation:

where:

α = 11*10^(-6) °C^-1

T₀ is the initial temperature, so T₀ = 2°C

T₁ is the final temperature, so T₁ = 35°C

L₀ is the initial length, so L₀ = 79

Replacing these in the equation we get:

ΔL = ( 11*10^(-6) °C^-1)*79*(35°C - 2°C)

     = 0.28677

So the length of the railroad will increase by 0.28677