Question

A metal rod of length 3m expand by 1cm when heated through 200 °cFind find the linear expansion coefficient of the metal

Answer 1

given, length of rod, l = 3m

expansion of rod, ∆l = 1cm = 0.01 m

temperature change , ∆T = 200°C

using formula, l' = l(1 + α∆T)

⇒l' = l + lα∆T

⇒(l' - l) = lα∆T

⇒∆l = lα∆T

⇒0.01 = 3 × α × 200

⇒0.01/600 = α

⇒α = (1/6) × 10^-4 /°C

⇒α = 0.1667 × 10^-4/°C = 1.667 × 10^-5/°C

hence, coefficient of linear expansion is 1.667 × 10^-5 /°C