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# A segment of steel railroad track has a length of 30,000 m when the temperature is 0,0 Celsius. What is the length when the temperature is 40 Celsius?

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 , ##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##.