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Q.

Coefficients of linear expansion of an isotropic solid along three rectangular axes in the solid are αx,αy and αz. Coefficient of cubical expansion of the solid for small change in temperature can be expressed as : ( assume αx,αy and αzto be small quantities)

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a

αx+αy+αz

b

αx αy αz

c

αx2+αy2+αz2

d

none of these

answer is A.

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Detailed Solution

αaverge =αX+αY+αZ3 so γ=3 αave =αx+αy+αz alternate method: V=lxlylz=lxo(1+αx∆T)lyo(1+αy∆T) lZo(1+αz∆T)     ≈lxolyolzo1+(αx+αy+αz)∆T      =Vo1+γ∆T
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