An aluminium bar of 8 m length and a steel bar of 5 mm longer in length are kept at 30°C. If the ambient temperature is raised gradually, at what temperature the aluminium bar will elongate 5 mm longer than the steel bar (the linear expansion coefficients for steel and aluminium are 12 × 10-6/°C and 23 × 10-6/°C respectively)?

An aluminium bar of 8 m length and a steel bar of 5 mm longer in length are kept at 30°C. If the ambient temperature is raised gradually, at what temperature the aluminium bar will elongate 5 mm longer than the steel bar (the linear expansion coefficients for steel and aluminium are 12 × 10-6/°C and 23 × 10-6/°C respectively)? Correct Answer 143.7°C 

Concept:

Change in length of a bar due to temperature difference is given by:

∆L = αL∆T

Calculation:

Given:

L_Al = 8 m = 8000 mm, L_S = 8005 mm,

α_Al  = 23 × 10^-6/°C, α_S = 12 × 10^-6/°C

T₁ = 30°C

Now,

Change in length in steel bar:

∆L_S = α_S L_S ∆T

= 12 × 10^-6 × 8005 × ∆T

∆L_S = 0.09606 × ∆T

Change in length in aluminium bar:

∆L_Al = 5 + ∆L_S + 5

αAl LAl ∆T = 10 + ∆LS

23 × 10^-6 × 8000 × ∆T = 10 + (0.09606 × ∆T)

∆T = 113.71

T₂ – 30 = 113.71

T₂ = 143.71 °C

Temperature at which aluminium bar will elongate 5 mm longer than the steel bar = 143.71°C