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