Thermal Expansion: Practice Problem & Solution
A solid cube of side \(4\text{ m}\) having coefficient of areal expansion \(2 \times 10^{-5}/^\circ\text{C}\). If temperature is changed by \(40^\circ\text{C}\) then the change in side length of the cube will be
Solution Explained:
To solve this problem, we apply the core principles of Thermal Expansion. Understanding the underlying formula is key to arriving at the correct answer below:
Coefficient of linear expansion is \(\alpha = \frac{\beta}{2} = 1 \times 10^{-5}/^\circ\text{C}\). Change in length \(\Delta L = L \alpha \Delta T = 4 \times (1 \times 10^{-5}) \times 40 = 1.6 \times 10^{-3}\text{ m} = 1.6\text{ mm}\).
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