Question:
When a copper sphere is heated, percentage change is
When a copper sphere is heated, percentage change is
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Volume coefficient of thermal expansion $\gamma = 3\alpha$ (linear). So percentage change in volume is 3 times that of radius for the same temperature rise.
Updated On: Apr 20, 2026
- maximum in radius
- maximum in volume
- maximum in density
- equal in radius, volume and density
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept:
The three coefficients of thermal expansion are related: \(\gamma = 3\alpha = 3\beta/2\), where \(\alpha\), \(\beta\), \(\gamma\) are linear, area, and volume expansion coefficients.
Step 2: Detailed Explanation:
Percentage change in radius \(= \alpha\Delta\theta\). Percentage change in volume \(= \gamma\Delta\theta = 3\alpha\Delta\theta\). Percentage change in density \(= -\gamma\Delta\theta/(1+\gamma\Delta\theta) \approx -3\alpha\Delta\theta\) in magnitude. Volume change is \(3\times\) radius change, and is numerically the largest positive change.
Step 3: Final Answer:
Percentage change is maximum in volume.
The three coefficients of thermal expansion are related: \(\gamma = 3\alpha = 3\beta/2\), where \(\alpha\), \(\beta\), \(\gamma\) are linear, area, and volume expansion coefficients.
Step 2: Detailed Explanation:
Percentage change in radius \(= \alpha\Delta\theta\). Percentage change in volume \(= \gamma\Delta\theta = 3\alpha\Delta\theta\). Percentage change in density \(= -\gamma\Delta\theta/(1+\gamma\Delta\theta) \approx -3\alpha\Delta\theta\) in magnitude. Volume change is \(3\times\) radius change, and is numerically the largest positive change.
Step 3: Final Answer:
Percentage change is maximum in volume.
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