What is the size of the force developing inside the steel rod when its temperature is raised by ∆T = 23.0 K?
A steel rod with a length of l = 1.55 m and a cross section of A = 3.02 cm2 is held fixed at the end points of the rod. What is the size of the force developing inside the steel rod when its temperature is raised by ∆T = 23.0 K? (The coefficient of linear expansion for steel is α = 1.17×10-5 1/K, the Young modulus of steel is E = 200 GPa.)
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Thermal expansion (∆L) is given by .. ∆L = Lo.α.∆θº ------ (1)
By Young's modulus .. E = F.Lo / A.∆L (in this case F is the force that resists an expansion ∆L .. keeping the rod at it's original length)
∆L = F.Lo / A.E ----- (2)
Equating (1) and (2) .. .. Lo.α.∆θº = F.Lo / A.E
F = A.E.α.∆θº
F = 3.02^-4 m² x 2.0^11 Pa x 1.17^-5 Kˉ¹ x 23 K .. .. .. ►F = 1.63^4 N