An anisotropic cuboid ABCDEFGH has linear expansion coefficients ax = 1e-5 /C (along x), ay = 2e-5 /C (along y) and az = 3e-5 /C (along z). The coefficient of superficial (areal) expansion of a face equals the sum of the two linear coefficients lying in that face. Which of the listed face values is correct?

beta = 5e-5 /C for the face spanned by the y and z directions
beta = 4e-5 /C for the face spanned by the x and z directions
beta = 3e-5 /C for the face spanned by the x and y directions
beta = 2e-5 /C for the face spanned by the x and z directions

Correct answer: beta = 5e-5 /C for the face spanned by the y and z directions

Solution

For a face, beta is the sum of the two in-plane linear coefficients. The y-z face gives ay + az = 2e-5 + 3e-5 = 5e-5 /C, which is the correct entry.

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