Question:
A copper rod and an iron rod of the same length have their temperature raised by the same amount. If the coefficient of linear expansion of copper is greater than that of iron, then
A copper rod and an iron rod of the same length have their temperature raised by the same amount. If the coefficient of linear expansion of copper is greater than that of iron, then
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Remember that thermal expansion depends on the material's coefficient of linear expansion, and this property can vary significantly between different materials.
Updated On: May 31, 2026
- Copper expands more than iron
- Iron expands more than copper
- Both expand by the same amount
- Expansion depends on their masses
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The Correct Option is A
Solution and Explanation
Step 1: Concept
The linear expansion of a material is directly proportional to its coefficient of linear expansion, temperature change, and original length. The formula for linear expansion is given by \(\Delta L = \alpha L_0 \Delta T\), where \(\Delta L\) is the change in length, \(\alpha\) is the coefficient of linear expansion, \(L_0\) is the original length, and \(\Delta T\) is the temperature change.
Step 2: Meaning
The question states that a copper rod and an iron rod have the same initial length and are heated by the same amount. The coefficients of linear expansion for these materials differ, with copper having a higher coefficient than iron.
Step 3: Analysis
Given: Both rods start with the same original length \(L_0\). They experience the same temperature change \(\Delta T\). The formula for the change in length due to thermal expansion is \(\Delta L = \alpha L_0 \Delta T\). Since both rods have the same initial length and are heated by the same amount, we can compare their expansions based on their coefficients of linear expansion. For copper: \[\Delta L_{\text{copper}} = \alpha_{\text{copper}} L_0 \Delta T\] For iron: \[\Delta L_{\text{iron}} = \alpha_{\text{iron}} L_0 \Delta T\] Given that the coefficient of linear expansion for copper (\(\alpha_{\text{copper}}\)) is greater than that for iron (\(\alpha_{\text{iron}}\)), it follows that: \[\Delta L_{\text{copper}} > \Delta L_{\text{iron}}\] This means the copper rod will expand more than the iron rod.
Step 4: Conclusion
The correct answer is A) Copper expands more than iron. Final Answer: (A)
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