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in Thermodynamics by (35 points)
the coefficient of linear expansion of an non isotropic metal bar are 1.8*10^-5 K^-1 along the x axis , 1.2*10^-5 K^-1 along the y axis ,and 1.7*10^-5 K^-1 along the z axis the coefficient of volume expansion of metal bar is

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+1 vote
by (36.5k points)
edited by

volume of non isotropic metal bar

V = l1.l2.l3 ---- (1)

\(\frac{dv}{vdt}\) = volume expansion cofficient

From equation (1) taking on both side

lnv = lnl + lnl2 + lnl3

Diffeciate equation (2) we get

\(\frac{1}{V} \frac{dv}{dt}\) = \(\frac{1}{l_1}\frac{dl_1}{dt}+\frac{1}{l_2}\frac{dl_2}{dt_2}+\frac{1}{l_3}\frac{dl_3}{dt_3}\)

∵ \(\frac{1}{V}\frac{dv}{dt}=\gamma\)

∵ \(\frac{1}{l}\frac{dl}{dt}=\alpha\)

γ = α1 + α2 + α3

γ = 1.8 x 10-5 + 1.2 x 10-5 + 1.7 x 10-5

γ = 4.7 x 10-5 k-1

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