The SI unit for the coefficient of linear expansion is

Options

A. `.^@C`
B. `"per".^@C`
C. `"cm"^2//.^@C`
D. none of these

Explanation

To determine the SI unit for the coefficient of linear expansion, we can follow these steps:

### Step 1: Understand the Concept
The coefficient of linear expansion (α) describes how the length of a material changes with temperature. It is defined as the change in length per unit length per degree change in temperature.

### Step 2: Write the Formula
The mathematical expression for the coefficient of linear expansion is given by:
\[ \alpha = \frac{\Delta L / L}{\Delta T} \]
where:
- \(\Delta L\) = change in length
- \(L\) = original length
- \(\Delta T\) = change in temperature

### Step 3: Identify the Units
- The unit of change in length (\(\Delta L\)) is typically measured in meters (m).
- The original length (L) is also measured in meters (m).
- The change in temperature (\(\Delta T\)) can be measured in degrees Celsius (°C) or Kelvin (K).

### Step 4: Simplify the Units
From the formula:
\[ \alpha = \frac{\Delta L / L}{\Delta T} \]
The units can be expressed as:
\[ \text{Units of } \alpha = \frac{\text{meters (m)}/\text{meters (m)}}{\text{degrees Celsius (°C)}} \]
This simplifies to:
\[ \text{Units of } \alpha = \frac{1}{\text{°C}} \text{ or } \frac{1}{\text{K}} \]

### Step 5: Conclusion
Thus, the SI unit for the coefficient of linear expansion is:
\[ \text{per degree Celsius (°C}^{-1}\text{) or per Kelvin (K}^{-1}\text{)} \]

### Final Answer
The SI unit for the coefficient of linear expansion is °C\(^{-1}\) or K\(^{-1}\).

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