Question

What is the length of the same rail road track on the cold winter day when the temperature is 0 degree Celsius

Answer 1

We know that

Length expansion formula

$L=L_{0}(1+\alpha\Delta T)$

$L=L_{0}(1+\alpha(T_{0}-T_{1}))\rightarrow(1)$

Where

$L_{0}=$ Initial length

$\alpha$ =linear expansion cofficient

$T_{1}=$ Final temperature

$T_{0}=$ initial temperature

Put T₀=0°c

$L=L_{0}(1+\alpha(0-T_{1}))$

$L=L_{0}(1-\alpha T_{1})$

$(L-L_{0})=-L_{0}\alpha T_{1}$

$\frac{L-L_{0}}{L_{0}}=-\alpha T_{1}\rightarrow(2)$

equation (2) repersent rail road track length is compressed of its initial length L₀