The unit of specific conductance is:

Options

A. `"ohm"^(-1)`
B. `"ohm"^(-1) cm^(-1)`
C. `"ohm"^(-2) cm^(2) eq^(-1)`
D. `"ohm"^(-1) cm^(2)`

Answer

To determine the unit of specific conductance, we can follow these steps:

### Step 1: Understand Specific Conductance
Specific conductance (also known as conductivity) is a measure of how well a solution can conduct electricity. It is denoted by the symbol \( \kappa \) (kappa).

### Step 2: Relate Conductance to Resistance
Conductance (G) is the reciprocal of resistance (R). Therefore, we can express this relationship as:
\[ G = \frac{1}{R} \]

### Step 3: Define Specific Conductance
Specific conductance is defined as the conductance of a unit volume of a solution. It can also be expressed in terms of resistivity (\( \rho \)):
\[ \kappa = \frac{1}{\rho} \]
where \( \rho \) is the resistivity of the material.

### Step 4: Relate Conductance to Geometry
The conductance of a conductor can be expressed in terms of its physical dimensions:
\[ G = \frac{A}{\rho L} \]
where:
- \( A \) = cross-sectional area (in cm²)
- \( L \) = length of the conductor (in cm)
- \( \rho \) = resistivity (in ohm-cm)

### Step 5: Rearrange for Specific Conductance
From the above equation, we can rearrange to find specific conductance:
\[ \kappa = \frac{G \cdot L}{A} \]

### Step 6: Determine the Units
Now, substituting the units into the equation:
- Conductance \( G \) has units of siemens (S), which is equivalent to ohm\(^{-1}\).
- Area \( A \) has units of cm².
- Length \( L \) has units of cm.

Thus, the units of specific conductance can be derived as follows:
\[ \text{Units of } \kappa = \frac{\text{S} \cdot \text{cm}}{\text{cm}^2} = \frac{\text{S}}{\text{cm}} = \text{S cm}^{-1} \]

### Step 7: Conclusion
Therefore, the unit of specific conductance is:
\[ \text{S cm}^{-1} \text{ or } \text{ohm}^{-1} \text{ cm}^{-1} \]

### Final Answer
The unit of specific conductance is \( \text{ohm}^{-1} \text{ cm}^{-1} \) or \( \text{S cm}^{-1} \).

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