The lenght of the railroad at 40°C is: #30,014.4m#
The formula that we need is the thermal dilatation formula:
#l_2=l_1(1+lambdaDeltaT)#,
where
#l_1# is the initial lenght,
#l_2# is the final lenght,
#lambda# is the coefficient of thermal expansion,
#DeltaT=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=30000m# ,
#l_2=Unknown#,
#lambda=1,2xx10^-5C^-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#.
