A metallic bar of Young's modulus 0.5×10¹¹ N m⁻² and coefficient of linear thermal expansion 10⁻⁵ °C⁻¹, length 1 m and area of cross-section 10⁻³ m² is heated from 0 °C to 100 °C without expansion or bending. The compressive force developed in it is:

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(2) 50×10³ N. Given: Y=0.5×10¹¹ N m⁻², α=10⁻⁵ °C⁻¹, L=1 m, A=10⁻³ m², Δ T=100 °C. Idea: the clamps hold the length fixed, so the expansion the heating would have produced is undone by an elastic compression of exactly the same size. Free expansion that is prevented: Δ L=Lα Δ T, so the strain forced on the bar is (Δ L)/L=α Δ T. α Δ T=10⁻⁵×100=10⁻³ Stress: σ=Yα Δ T=0.5×10¹¹×10⁻³=0.5×10⁸ N m⁻² Force: F=σ A=0.5×10⁸×10⁻³=0.5×10⁵ N F=50×10³ N

A metallic bar of Young's modulus 0.5×10¹¹ N m⁻² and coefficient of linear thermal expansion 10⁻⁵ °C⁻¹, length 1 m and area of cross-section 10⁻³ m² is heated from 0 °C to 100 °C without expansion or bending. The compressive force developed in it is:

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