If a substance contracts on heating, its coefficient of linear expansion is

Options

A. `+ve`
B. `-ve`
C. zero
D. infinity

Answer

To determine the coefficient of linear expansion of a substance that contracts upon heating, we can follow these steps:

### Step 1: Understand the Coefficient of Linear Expansion
The coefficient of linear expansion (α) is defined as the change in length per unit length per degree change in temperature. Mathematically, it is expressed as:
\[ \alpha = \frac{\Delta L / L}{\Delta T} \]
where:
- \( \Delta L \) = change in length
- \( L \) = original length
- \( \Delta T \) = change in temperature

### Step 2: Analyze the Situation
In this case, we are told that the substance contracts when it is heated. This means that as the temperature increases, the length of the substance decreases.

### Step 3: Identify the Signs of Changes
When a substance contracts:
- The change in length (\( \Delta L \)) is negative because the length decreases.
- The change in temperature (\( \Delta T \)) is positive because the temperature is increasing.

### Step 4: Substitute Values into the Formula
Substituting the signs into the equation for the coefficient of linear expansion:
\[ \alpha = \frac{\Delta L}{L \cdot \Delta T} \]
Since \( \Delta L \) is negative and \( \Delta T \) is positive, we have:
\[ \alpha = \frac{\text{negative}}{\text{positive}} = \text{negative} \]

### Step 5: Conclusion
Thus, if a substance contracts upon heating, its coefficient of linear expansion is negative.

### Final Answer
The coefficient of linear expansion of a substance that contracts on heating is **negative**.

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