Question

A non-isotropic solid metal cube has coefficients of linear expansion as : 5 × 10^–5/°C along the x-axis and 5 × 10^–6/°C along the y and the z-axis. If the coefficient of volume expansion of the solid is C × 10^–16/°C then the value of C is ______. 

Answer 1

Let the initial cube has sides l₁​,l₂​ and l₃​ in x,y,z direction respectively.
Initial volume =l₁​l₂​l₃​.........(A)

Let change in volume be ΔV

then, the coefficient of volume expansion is given by:

Answer 2

γ = α_x + α_y + α_z

= 5 × 10^–5 + 5 × 10^–6 + 5 × 10^–6

= (50 + 5 + 5) × 10^–6

γ = 60 × 10^–6

C = 60.