# Question 9c6a4

Jan 29, 2015

The lenght of the railroad at 40°C is: $30 , 014.4 m$

The formula that we need is the thermal dilatation formula:

${l}_{2} = {l}_{1} \left(1 + \lambda \Delta T\right)$,

where
${l}_{1}$ is the initial lenght,
${l}_{2}$ is the final lenght,
$\lambda$ is the coefficient of thermal expansion,
$\Delta T = {T}_{2} - {T}_{1}$ is the amount of incresing (if it is positive) or decresing (if it is negative) of the temperature.

So, in this case:

${l}_{1} = 30000 m$ ,
${l}_{2} = U n k n o w n$,
$\lambda = 1 , 2 \times {10}^{-} 5 {C}^{-} 1$ (steel)
DeltaT=T_2-T_1=(40-0)°C=40°C.

So:
l_2=30000m(1+1,2xx10^-5°C^-1xx40°C)=30000m(1.00048)=30014,4m#.