Question

An anisotropic material has coefficient of linear expansion α, 2α, 2α along x, y and z-axis respectively. The coefficient of cubical expansion is​

Answer 1

Answer:

An anisotropic material has coefficient of linear expansions as a, 2a and 3/2 a along x,y and z axis respectively. The coefficient of cubical expansion is 3a.

Explanation:

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Answer 2

The Main Answer is: The coefficient of volume expansion is 5α.

Given: coefficient of linear expansion along x-axis ($\alpha _{x}$) = α

           coefficient of linear expansion along y-axis ($\alpha_{y}$) = 2α

           coefficient of linear expansion along z-axis ($\alpha _{z}$) = 2α

To Find: Coefficient of volume expansion

Solution:

An anisotropic material is a material where the properties are not uniform in all directions. Thus, as given in the question, these materials expand differently in different directions.

$\alpha _{x}$ = α

$\alpha_{y}$ = 2α

$\alpha _{z}$ = 2α

We know,

The coefficient of volume expansion (γ) is the scalar sum of the coefficients of linear expansion in all directions.

Mathematically,

γ = $\alpha _{x}$ + $\alpha_{y}$ + $\alpha _{z}$

γ = α +2α + 2α = 5α

Therefore, the coefficient of volume expansion (γ) = 5α

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