Question

The volume of a block of metal at \(30^\circ\text{C}\) changes by \(0.12\%\) when its temperature is increased to \(70^\circ\text{C}\). The coefficient of linear expansion of the metal is

• A. \(2 \times 10^{-5} /^\circ\text{C}\)
• B. \(3 \times 10^{-5} /^\circ\text{C}\)
• C. \(4 \times 10^{-5} /^\circ\text{C}\)
• D. \(1 \times 10^{-5} /^\circ\text{C}\)

Hint:

Relation: $\beta = 3\alpha$

Answer 1

The Correct Option is D

Concept: \[ \frac{\Delta V}{V} = 3\alpha \Delta T \]

Step 1: Given data. \[ \frac{\Delta V}{V} = 0.12\% = 0.0012 \quad , \quad \Delta T = 70 - 30 = 40^\circ C \]

Step 2: Substitute. \[ 0.0012 = 3\alpha \times 40 \]

Step 3: Solve. \[ \alpha = \frac{0.0012}{120} = 1 \times 10^{-5} \]

Step 4: Conclusion.
\[ \alpha = 1 \times 10^{-5} /^\circ C \] Final Answer: Option (D)