if the coefficient of linear expansion is 10-4 then find 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 cubical expansion is typically three times the coefficient of linear expansion. This relationship arises because volume expansion involves changes in all three dimensions of an object, while linear expansion only considers one dimension.

Understanding the Relationship

The coefficient of linear expansion (α) measures how much a material expands per degree change in temperature along a single dimension. The coefficient of cubical expansion (β), on the other hand, measures the change in volume per degree change in temperature. The mathematical relationship can be expressed as:

• β = 3α

Applying the Formula

Given that the coefficient of linear expansion is 10^-4 per degree Celsius, we can substitute this value into the formula:

• α = 10^-4 per °C
• β = 3 × (10^-4)
• β = 3 × 10^-4 per °C

Final Calculation

Now, performing the multiplication gives:

• β = 3 × 10^-4 = 3 × 0.0001 = 0.0003

Thus, the coefficient of cubical expansion is 3 × 10^-4 per degree Celsius.

Real-World Implications

This relationship is crucial in various applications, such as engineering and materials science, where understanding how materials expand and contract with temperature changes is essential for designing structures and components that can withstand thermal stresses.

In summary, if the coefficient of linear expansion is 10^-4, the coefficient of cubical expansion is 3 × 10^-4 per degree Celsius. This simple yet powerful relationship helps us predict how materials behave under temperature variations.