Question

A brass rod of length 50cm and diameter 3.0 mm is Joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at 250°C, if the original lengths are at 40.0°C? Is there a ‘thermal stress’ developed at the junction? The ends of the rod are free to expand (Coefficient of linear expansion of brass = 2.0 × 10^-5K^-1, steel = 1.2 × 10^-5K^-1 ).

Answer 1

Given: l_brass = 50cm, l_steel = 50cm

T₁ = 40°C = 313K

T₂ = 250°C = 523 K

α_brass = 2.0 × 10^-5K^-1

α_steel = 1.2 × 10^-5K^-1

∆l_brass = l_brass × α_brass × ∆T

= 50 × 2.0 × 10^-5 × (523 – 313)

∆l_brass = 0.21 cm

∆l_steel = l_steel × α_steel × ∆T

= 50 × 1.2 × 10^-5 × (523 – 313)

= 0.126 cm

∆l_steel = 0.13cm

(round off to two significant figures) Since the rods are free to expand, no thermal stress is developed at the junction.