if the coefficient of linear expasion is 10-4/c then find the coefficient of cubical expansion

To find the coefficient of cubical expansion when you know the coefficient of linear expansion, you can use a straightforward relationship between the two. The coefficient of linear expansion (α) is related to the coefficient of cubical expansion (β) by the formula:

Understanding the Relationship

The relationship is given by:

• β = 3α

This means that the coefficient of cubical expansion is three times the coefficient of linear expansion. This relationship holds because when an object expands in three dimensions, each linear dimension contributes to the overall volume change.

Applying the Given Value

In your case, the coefficient of linear expansion is given as:

• α = 10^-4 / °C

Now, substituting this value into the formula for cubical expansion:

Calculating the Coefficient of Cubical Expansion

Using the formula:

• β = 3α = 3 × 10^-4 / °C

Now, performing the multiplication:

• β = 3 × 10^-4 = 3 × 10^-4 / °C

Final Result

Thus, the coefficient of cubical expansion is:

• β = 3 × 10^-4 / °C

This means that for every degree Celsius increase in temperature, the volume of the material will increase by three times the linear expansion coefficient, which is a significant factor to consider in applications involving thermal expansion.