Question

Railway lines are laid with gaps to allow for expansion. If the gap between steel rails 66 m long is 3.63 cm at 10 degree celsious then at what temperature will the lines just touch

Answer 1

One railway line should be extended by 3.36/2 = 1.68 cm = 0.0168 m

Let at temperature T2 lines just touch .  
Here , L1=66 m  , T1= 10°C         
Coficient of linear expansion (α) =11×10−6C−1L2=66 m +0.0168 
m=66.0168 
mL2=L1[1+α(T2−T1)]66.0168
=66[1+(11×10−6)(T2−10)]66.016866
=1+(11×10−6)(T2−10)66.016866−1
=(11×10−6)(T2−10)0.016866
=(11×10−6)(T2−10)0.0168×10666×11
=(T2−10)16800726+10
=T223.14+10
=T2
The temperature at which the rails just is 23.14°C