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?
February 20th, 2023
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##.