Question

The coefficient of linear expansion of aluminum is \( 2.5 \times 10^{-5} \, {K}^{-1} \). Its coefficient of volume expansion in \( {K}^{-1} \) is:

• A. \( 1.25 \times 10^{-5} \)
• B. \( 5.0 \times 10^{-5} \)
• C. \( 7.5 \times 10^{-5} \)
• D. \( 1 \times 10^{-4} \)
• E. \( 4.0 \times 10^{-5} \)

Hint:

For isotropic materials, the volume expansion coefficient is **three times** the linear expansion coefficient.

Answer 1

The Correct Option is C

The coefficient of volume expansion (\( \beta \)) is related to the coefficient of linear expansion (\( \alpha \)) by: \[ \beta = 3\alpha \] Substituting \( \alpha = 2.5 \times 10^{-5} \): \[ \beta = 3 \times 2.5 \times 10^{-5} = 7.5 \times 10^{-5} { K}^{-1} \]