Question

Railway lines are laid with gaps to allow for expansion. If the gap between steel rails 66m long, is 3.63 at 10 degree celcius, then at what temperature will the lines just touch. Given: Coefficient of Linear expansion of steel: 11 x 10^-6

Answer 1

Given: Gap between the steel rail is = 66 m

           dl = 0.0363 m

           Temperature is equal to 10°

           coefficient of linear expansion of steel α = 11 x 10^-6

To find: At what temperature will the lines be just touched?

Solution:

• So, to find that at what temperature the lines will touch, we have the formula

                dl/l = αΔT

                dl/l = α(T1-T2)

• So now putting all the given values in the above equation, we get:

                0.0363 / 66 = 11 x 10^-6 x (T - 10)

• So further calculating, the value of T comes out to be:

                T = { 0.0363 /  66 x 11 x 10^-6 } + 10

                T = { 0.0363 /  726 x 10^-6 }  + 10

• So, after solving  T comes out to be 60°

Answer:

         At 60° temperature the lines will just touch.

Answer 2

Given:

1. Length of steel rails = 66m

2. The gap between steel rails = 3.63

3. Temperature = 10° C

4. Linear expansion of steel = 11 x 10⁻⁶

To find:

The temperature at which the lines just touch.

Solution:

• We know that, dl/dt = αΔT

• Substituting the values, we get,

$\dfrac{0.0363}{66}=11\times10^{-6}\times{T-10}$

$T=\dfrac{0.0363}{66\times11\times10^{-6}}+10$

T = 60°

• Thus, the lines will touch at 60°.