Question

A steel pipe 36.0 m long, installed when the temperature was is used to transport superheated steam at a temperature of 155 oC. Steel's coefficient of linear expansion is 1.2E-5 K-1. The pipe is allowed to expand freely when the steam is transported.

What is the increase in the length of the pipe when it is used with the superheated steam? mm.

Answer 1

60.48mm

Step-by-step explanation:

This question is base on the topic " Thermal expansivity".

Linear expansivity (α) of a substance is defined as the increase in length per unit length per degree rise in temperature.

α =
`(L_(2) - L_(1) )/(L_(1) ( ∅_(2) - ∅_(1)) )`

make L₂ the subject of formula.

L₂=L₁(1+Δ∅α), where Δ∅ is the temperature difference i.e ∅₂ - ∅₁

Now expand the equation

we have : L₂ = L₁ + L₁Δ∅α

L₂ - L₁ = L₁Δ∅α

L₂ - L₁ = 36m x 1.2E-5 x 36 x (155-15)

L₂ - L₁ = 0.06048m; Convert to mm by multiplying by 1000

L₂ - L₁ = 60.48mm

L₂-L₁ = Increased length

L₂ = Final length

L₁ = Initial length

α = Steel's coefficient of linear expansion

Δ∅ = Temperature difference i.e 155 oC - 15oC = 140oC