Question

A metal wire 19 m long is cooled from 41 to -3°C. How much of a change in length will the wire experience if the coefficient of thermal expansion for this metal is 21 x 10-6 (°C)-1? If the change in length is negative (i.e., the wire shrinks), insert a minus sign before the numerical answer.

Answer 1

ΔL = - 0.017556 m

Step-by-step explanation:

Given

L₀ = 19 m

T₀ = 41ºC

T₁ = -3ºC

α = 21*10⁻⁶ °C⁻¹

ΔL = ?

We can use the equation

ΔL = L₀*α*ΔT

where

ΔT = T₁ - T₀ = -3ºC - 41ºC

⇒ ΔT = -44ºC

then

ΔL = (19 m)*(21*10⁻⁶ °C⁻¹)*(-44ºC)

⇒ ΔL = - 0.017556 m