A unit scale is to be prepared whose length does not change with temperature and remains 20 cm, using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way that the difference between their lengths remains constant. If the lengt…

Question

A unit scale is to be prepared whose length does not change with temperature and remains 20 cm, using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way that the difference between their lengths remains constant. If the length of brass is 40 cm, the length of iron will be cm. (αᵢᵣₒₙ=1.2×10⁻⁵ K⁻¹ and α_brass=1.8×10⁻⁵ K⁻¹)

Accepted Answer

60. Idea: the scale is the gap between the two free ends, so its length is L_Fe-L_Br; that difference stays fixed only if the two pieces expand by exactly the same amount. L_Feα_FeΔ T=L_Brα_BrΔ T, so L_Feα_Fe=L_Brα_Br. L_Fe=(L_Brα_Br)/(α_Fe)=(40×1.8×10⁻⁵)/(1.2×10⁻⁵)=60 cm. Check the scale length: 60-40=20 cm, exactly as required. The piece with the smaller α has to be the longer one, so iron is 60 cm.

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