Potential energy U = Average force * Increase in length = 1 / 2 FΔl = 1 / 2 Stress * Strain * Volume of the wire Elastic potential energy per unit volume
U = 1 / 2 * Stress * Strain = 1 / 2 ( Young ’ s modulus ) * ( Strain ) 2 Elastic potential energy of a stretched spring = 1 / 2 kx 2 where , k = Force constant of spring and x = Change in length . Thermal Stress
When temperature of a rod fixed at its both ends is changed , then the produced stress is called thermal stress .
Thermal stress = F / A = yαΔθ where , α = coefficient of linear expansion of the material of the rod .
When temperature of a gas enclosed in a vessel is changed , then the thermal stress produced is equal to change in pressure ( Δp ) of the gas .
Thermal stress = p = Ky θ where , K = bulk modulus of elasticity and γ = coefficient of cubical expansion of the gas . Interatomic force constant K = Yro where , ro = interatomic distance .