Question

A cuboid ABCDEFGH is anisotropic with a_x = 1 × 10^–5/ŗC, a_y = 2 × 10^–5/ŗC, a_z = 3 × 10^–5/ŗC. Coefficient of superficial expansion (b) of faces can be (Take approximation)

• A. b_ABCD = 5 × 10^–5/ŗC
• B. b_BCGH = 4 × 10^–5/ŗC
• C. b_CDEH = 3 × 10^–5/ŗC
• D. b_EFGH = 2 × 10^–5/ŗC

Answer 1

Answer: (C)

b_CDEH = 3 × 10^–5/ŗC

Answer 2

l_x = $\mathcal{l}_{x_{0}}$ (1 + a_xT), l_y = $\mathcal{l}_{y_{0}}$ ( 1 + a_yT)

l_xl_y = $\mathcal{l}_{y_{0}}$ [1 + (a_x + a_y + a_x a_y)T]

A_x = $A_{x_{0}}$ [1 + (a_x + a_y + a_xa_y)T]

A_x = $A_{x_{0}}$ [1 + (1 × 10^–5 + 2 × 10^–5 + 1 × 2 × 10^–10)T]

A_x =$A_{x_{0}}$ [1 + 3 × 10^–5T],

b_CDEH = 3 × 10^–5/ŗC