The unit for the coefficient of apparent expansion is

Options

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

Answer

To find the unit for the coefficient of apparent expansion, we can follow these steps:

### Step 1: Understand the Concept
The coefficient of apparent expansion refers to the increase in volume of a liquid per unit original volume for each degree rise in temperature.

### Step 2: Define the Coefficient of Apparent Expansion
The coefficient of apparent expansion (denoted as \( \beta \)) is defined mathematically as:
\[ \beta = \frac{\Delta V / V_0}{\Delta T} \]
where:
- \( \Delta V \) = change in volume
- \( V_0 \) = original volume
- \( \Delta T \) = change in temperature (in degrees)

### Step 3: Analyze the Units
From the definition:
- The change in volume \( \Delta V \) has units of volume (e.g., cubic meters, \( m^3 \)).
- The original volume \( V_0 \) also has units of volume (e.g., cubic meters, \( m^3 \)).
- The change in temperature \( \Delta T \) has units of temperature (e.g., degrees Celsius, \( °C \)).

### Step 4: Simplify the Units
When we calculate \( \frac{\Delta V}{V_0} \), the units of volume cancel out:
\[ \frac{\Delta V}{V_0} \text{ has no units (dimensionless)} \]
Thus, the units for the coefficient of apparent expansion become:
\[ \beta = \frac{\text{dimensionless}}{\Delta T} = \frac{1}{°C} \]

### Step 5: Final Unit
Therefore, the unit for the coefficient of apparent expansion is:
\[ \text{per degree Celsius} \text{ or } °C^{-1} \]

### Conclusion
The unit for the coefficient of apparent expansion is \( °C^{-1} \) or per degree Celsius.

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