First slide

Thermal expansion

Question

The coefficient of expansion of a crystal in one direction (x-axis) is 2.0x 10^-6 K^-1 and that in the other two perpendicular (y-and z-axes) direction is 1.6 x 10^-6 K^-1 What is the coefficient of cubical expansion of the crystal?

Moderate

A

$1.6 \times 10^{- 6} K^{- 1}$
B

$1.8 \times 10^{- 6} K^{- 1}$
C

$2.0 \times 10^{- 6} K^{- 1}$
D

$5.2 \times 10^{- 6} K^{- 1}$

Solution

Coefficient of cubical expansion is
$γ = α_{x} + α_{y} + α_{z} = α_{x} + 2 α_{y}$ $(∵ α_{y} = α_{z})$
$= 2.0 \times 10^{- 6} + 2 \times 1.6 \times 10^{- 6} = 5.2 \times 10^{- 6} K^{- 1}$
Hence the correct choice is (4).

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