Question

A steel rod (Y = 2.0 × 10¹¹ Nm^–2; and α = 10^–50 C^–1) of length 1 m and area of cross-section 1 cm² is heated from 0°C to 200°C, without being allowed to extend or bend. What is the tension produced in the rod?

Answer 1

Because of the increase in temperature the increase in length per unit length of the rod is

Δl/l_o = αΔT = 10^-5 x 2 x 10^-2 = 2 x 10^-3

Let the compressive tension on the rod be T and the cross sectional area be a, then