A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of the increase in temperature. The length of the aluminium rod is (α_Cu=1.7×10⁻⁵ K⁻¹, α_Al=2.2×10⁻⁵ K⁻¹)

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(1) 68 cm. Given: l_Cu=88 cm, α_Cu=1.7×10⁻⁵ K⁻¹, α_Al=2.2×10⁻⁵ K⁻¹. Idea: the difference in length is fixed at every temperature only if the two rods lengthen by exactly the same amount, so Δ l_Cu=Δ l_Al. l_Cuα_CuΔ T=l_Alα_AlΔ T l_Al=(l_Cuα_Cu)/(α_Al)=(88×1.7×10⁻⁵)/(2.2×10⁻⁵) l_Al=(149.6)/(2.2)=68 cm

A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of the increase in temperature. The length of the aluminium rod is (α_Cu=1.7×10⁻⁵ K⁻¹, α_Al=2.2×10⁻⁵ K⁻¹)

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