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

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