The unit for the coefficient of real expansion is

Options

A. cm
B. `cm//.^@C`
C. `cm.^@C`
D. `//.^@C`

Answer

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

### Step-by-Step Solution:

1. **Understand the Coefficient of Real Expansion**:
- The coefficient of real expansion of a liquid is defined as the ratio of the change in volume (ΔV) to the original volume (V) of the liquid per unit change in temperature (ΔT).

2. **Write the Formula**:
- The formula for the coefficient of real expansion (β) can be expressed as:
\[ \beta = \frac{\Delta V / V}{\Delta T} \]

3. **Analyze the Components**:
- Here, ΔV is the change in volume, V is the original volume, and ΔT is the change in temperature (in degrees Celsius or Kelvin).

4. **Identify the Units**:
- The change in volume (ΔV) has units of volume (e.g., cm³).
- The original volume (V) also has units of volume (e.g., cm³).
- Therefore, the ratio ΔV/V is dimensionless (it has no units).
- The change in temperature (ΔT) is measured in degrees Celsius (°C) or Kelvin (K).

5. **Combine the Units**:
- Since ΔV/V is dimensionless, the unit of the coefficient of real expansion is simply the unit of temperature change, which is per degree Celsius (°C) or per Kelvin (K).

6. **Conclusion**:
- Therefore, the unit for the coefficient of real expansion is:
\[ \text{per degree Celsius (°C}^{-1}\text{) or per Kelvin (K}^{-1}\text{)} \]

### Final Answer:
The unit for the coefficient of real expansion is **per degree Celsius (°C⁻¹)**.