A crystal has a coefficient of expansion 13 × 10 – 9 in one direction and 231 × 10– 9 in every direction at right angles to it. Then the cubical coefficient of expansion is :

Engineering

Physics

Thermal Expansion

Question

A crystal has a coefficient of expansion 13 × 10^{– 9} in one direction and 231 × 10^{– 9} in every direction at right angles to it. Then the cubical coefficient of expansion is :

4.62 × 10^{– 7}

4.75 × 10^{– 7}

2.44 × 10^{– 7}

2.57 × 10^{– 7} s

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The cubical coefficient of expansion (γ) is the sum of the linear coefficients in three perpendicular directions. Given α₁ = 13 × 10^–9 and α₂ = α₃ = 231 × 10^–9, the formula is:

$γ = α_{1} + α_{2} + α_{3}$

Substituting the values: γ = (13 + 231 + 231) × 10^–9 = 475 × 10^–9 = 4.75 × 10^–7.

Final Answer: 4.75 × 10^–7