Question

A steel railroad track has a length of 40 m when the temperature is −5 ◦C. What is the increase in the length of the rail on a hot day when the temperature is 35 ◦C? The linear expansion coefficient of steel is 11 × 10−6 ( ◦C)−1 . Answer in units of m.

Answer 1

Answer:

0.0176m

Explanation:

Given that,

railroad track has a length of 40 m

temperature is T₁ −5 ◦C

temperature is T₂ 35 ◦C

linear expansion coefficient of steel is 11 × 10−6 ( ◦C)−1

Lo = 40 m

T₁ = -5° C

T₂ = 35° C

dT = T₂ - T₁

    = 35 - (-5)

     = 40°C

L = Lo*(1+alpha*dT)

dL = Lo*alpha*dT

dT =  40°C

alpah = 11 x 10⁻⁶

Lo = 40 m

dL = 40 × 11 x 10⁻⁶  × 40

 = 0.0176m

Answer 2

Answer:

ΔL = 0.0176m

Explanation:

We are given;

Length of railroad track; L = 40 m

First Temperature; T1 = −5 ◦C

Second temperature; T2 = 35 ◦C

linear expansion coefficient of steel; α = 11 × 10^(−6) (◦C)^(-1)

The increase in length is given by the equation;

ΔL = α•L•ΔT

Where,

α is linear coefficient

L is length

ΔT is change in temperature.

ΔT = first temperature - Second Temperature

Thus, ΔT = 35 - (-5) = 35 + 5 = 40°C

Thus,plugging in relevant values,

ΔL = α•L•ΔT = 11 × 10^(−6)•40•40

ΔL = 0.0176m