thermal expansion

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two steel rods and an aluminium rod of equal length l₀ and equal cross section are joined rigidly at their ends a sshown in the figure below. all the rods are in a state of zero tension at 0⁰C.
Find the length of the system when the temperature is raised to Î¸.Coefficient of linear expansion of aluminium and steel are Î±_a and Î±_s respectively. young's modulus of aluminium is Y_aand that of steel is Y_s.

#Physics #Thermal physics

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1 Answers

33

Abhishek Priyam ·2009-03-19 05:50:47

Well...

Let dl be change in length...

starin in steel is (dls-dl)/l₀
strain in Al is (dl-dl_Al)/l₀

Now 2(dls-dl)/l₀Y_sA=(dl-dl_Al)/l₀Y_AlA

dls=l₀Î±_sÎ”Î¸
dl_Al=l₀Î±_AlÎ”Î¸

solve to get dl+l₀

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