Question

a steel railroad track has a length of 30m when the temperature is 2 degrees celsius. what is the increase in the length of the rail on a hot day when the temperature is 38 degrees celsius? the linear expansion coefficient of steel is 11 x 10^ -6 (c)^-1

Answer 1

Answer:

Correct answer:  L₂ = 30.012 m

Explanation:

Given:

L₁ = 30 m initial length on the temperature t₁ = 2 C°

L₂ = ?   final length on the temperature t₂ = 38 C°

α = 11 · 10⁻⁶ C⁻¹ the linear expansion coefficient of steel

The formula by which we will calculate the new rail length is:

L₂ = L₁ · ( 1 + α · (t₂ - t₁))

L₂ = 30 · ( 1 + 11 · 10⁻⁶ · ( 38 - 2)) = 30 · ( 1 + 11 · 10⁻⁶ · 36) = 30 · (1 + 0.000396)

L₂ = 30 · 1.0004 = 30.012 m

L₂ = 30.012 m

God is with you!!!

Answer 2

The increase in length is 0.012 m

Linear Expansion due to rise in temperature in given by:

ΔL = LαΔT

here ΔL is the increase in length due to change in temperature ΔT.

α = coefficient of linear expansion

Given that,  α = $11*10^{-6}C^{-1}$ , L =30 m, and ΔT = 38-2 = 36°C

so,      ΔL = 30 × $11*10^{-6}C^{-1}$ × 36

         ΔL = 0.012 m is the increase in length.

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