Question:
If we consider a rectangular sheet of the solid, the coefficient of areal expansion is:
If we consider a rectangular sheet of the solid, the coefficient of areal expansion is:
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For solids, coefficient of area expansion \(\beta \approx 2 \alpha\) and coefficient of volume expansion \(\gamma \approx 3 \alpha\), neglecting higher order terms.
Updated On: Jun 19, 2026
- Half of its coefficient of linear expansion
- Thrice of its coefficient of linear expansion
- Twice of its coefficient of linear expansion
- Square root of its coefficient of linear expansion
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The Correct Option is C
Solution and Explanation
Step 1: Recall relation between linear and areal expansion.
For a solid sheet of area \(A = L \cdot W\), if linear expansion coefficient is \(\alpha\): \[ \Delta L = \alpha L \Delta T, \quad \Delta W = \alpha W \Delta T \]
Step 2: Calculate change in area.
\[ \Delta A = (L + \Delta L)(W + \Delta W) - LW \approx LW(2 \alpha \Delta T) \] Neglect \((\alpha \Delta T)^2\) term.
Step 3: Areal expansion coefficient.
\[ \beta = \frac{\Delta A}{A \Delta T} = 2 \alpha \]
Step 4: Conclusion.
The coefficient of areal expansion is twice the linear expansion coefficient.
For a solid sheet of area \(A = L \cdot W\), if linear expansion coefficient is \(\alpha\): \[ \Delta L = \alpha L \Delta T, \quad \Delta W = \alpha W \Delta T \]
Step 2: Calculate change in area.
\[ \Delta A = (L + \Delta L)(W + \Delta W) - LW \approx LW(2 \alpha \Delta T) \] Neglect \((\alpha \Delta T)^2\) term.
Step 3: Areal expansion coefficient.
\[ \beta = \frac{\Delta A}{A \Delta T} = 2 \alpha \]
Step 4: Conclusion.
The coefficient of areal expansion is twice the linear expansion coefficient.
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