If an isotropic solid has coefficients of linear expansion `alpha_(x),alpha_(y) and alpha_(z)`for three mutually perpendicular directions in the solid, what is the coefficient of volume expansion for the solid?

Explanation

To find the coefficient of volume expansion for an isotropic solid with coefficients of linear expansion \( \alpha_x, \alpha_y, \) and \( \alpha_z \) in three mutually perpendicular directions, we can follow these steps:

### Step 1: Understand the Concept of Linear Expansion
The linear expansion of a solid in a particular direction is given by the formula:
\[ L' = L(1 + \alpha \Delta T) \]
where \( L' \) is the final length, \( L \) is the original length, \( \alpha \) is the coefficient of linear expansion, and \( \Delta T \) is the change in temperature.
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