Railway lines, 25 m long, are being laid when the temperature is 15°C. Gaps of 1.8 cm are being left between them. If α = 12×10^-6/^°C, the temperature at which they will touch each other is ______

Concept:

It is a case of restricted expansion, so the stress is given as,

\(σ =\left[ {\frac{{L \propto {\bf{Δ }}T - δ a}}{L}} \right]E\)

where, σ = thermal stress produced, L = length of rail, α = coefficient of thermal expansion, ΔT = temperature difference,δa = gap between two rails, E = youngs modulus

The expansion on the bar due to the increase in temperature

ΔLth = α × ΔT × L 

Calculation:

Given:

α = 12 × 10-6/°C, L = 25 m, T₁ = ?, T₂ = 15°C, ΔLth = 1.8 cm = 0.018 m

0.018 = 12 × 10-6 × (T₁ - 15) × 25

(T1 - 15) = 60

T1 = 75°C