Two rods, one of iron and the other of aluminium, are heated to the same temperature. Then,

Options

A. the iron rod will expand less
B. the iron rod will expand more
C. both rods will expand equally
D. the iron rod will not expand at all

Answer

To solve the question regarding the expansion of two rods (one made of iron and the other made of aluminum) when heated to the same temperature, we will follow these steps:

### Step 1: Understand the Concept of Thermal Expansion
When materials are heated, they tend to expand. The amount of expansion depends on the material's coefficient of linear thermal expansion (α), which is a measure of how much a material expands per degree of temperature change.

### Step 2: Identify the Coefficients of Linear Thermal Expansion
- For aluminum, the coefficient of linear thermal expansion (α) is approximately \(25 \times 10^{-6} \, \text{°C}^{-1}\).
- For iron, the coefficient of linear thermal expansion (α) is approximately \(11.7 \times 10^{-6} \, \text{°C}^{-1}\).

### Step 3: Compare the Coefficients
Since the coefficient of thermal expansion for aluminum is greater than that for iron, it implies that aluminum will expand more than iron when both are heated to the same temperature.

### Step 4: Apply the Formula for Linear Expansion
The formula for linear expansion is given by:
\[ \Delta L = L_0 \cdot \alpha \cdot \Delta T \]
Where:
- \(\Delta L\) is the change in length,
- \(L_0\) is the original length,
- \(\alpha\) is the coefficient of linear thermal expansion,
- \(\Delta T\) is the change in temperature.

### Step 5: Analyze the Expansion
Since both rods are heated to the same temperature, the change in temperature (\(\Delta T\)) is the same for both rods. However, because aluminum has a higher coefficient of linear thermal expansion, it will expand more than iron.

### Conclusion
Therefore, the correct answer is that the iron rod will expand less than the aluminum rod.

### Final Answer
The iron rod will expand less than the aluminum rod.

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