Question

If we consider a rectangular sheet of the solid, the coefficient of areal expansion is:

• A. Half of its coefficient of linear expansion
• B. Thrice of its coefficient of linear expansion
• C. Twice of its coefficient of linear expansion
• D. Square root of its coefficient of linear expansion

Hint:

For solids, coefficient of area expansion \(\beta \approx 2 \alpha\) and coefficient of volume expansion \(\gamma \approx 3 \alpha\), neglecting higher order terms.

Answer 1

The Correct Option is C

Step 1: Relating linear and area expansion.
For a sheet, area A = L·W. With linear coefficient α, ΔL = αLΔT and ΔW = αWΔT.

Step 2: Change in area.
ΔA ≈ 2α A ΔT (neglecting the (αΔT)² term).

Step 3: Areal coefficient definition.
β = ΔA/(A ΔT) = 2α.

Step 4: Conclusion.
The coefficient of areal expansion is twice the linear expansion coefficient.