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Give the formula for relation between Young’s modulus coefficient of linear expansion and thermal stress?

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Metal rod either expands or contract on heating or cooling. A stress is produced in rod if it is restricted from expanding or contracting. This stress is directly proportional to the thermal strain.

Thermal strain = Change in length / original length
Thermal strain = Δ L / L

Thermal strain = α L ΔT / L —— Linear thermal expansion (Δ L = α L ΔT).
Thermal strain = α ΔT

Young’s modulus of material = Stress / Strain
Y = Stress / α ΔT
So Stress = Y α ΔT

Therefore, Force = Y  A α ΔT

Y = Young’s modulus of elasticity
α = coefficient of linear expansion.
∆T = increase in temperature
A = Area

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