The unit of thermal conductivity is :

Options

A. `W m^(-1) K^(-1)`
B. `J m^(-1) K^(-1)`
C. `J m^(-1) K^(-1)`
D. `W m K^(-1)`

Explanation

To find the unit of thermal conductivity, we start with the formula for thermal conductivity (K):

\[ K = \frac{Q \cdot D}{A \cdot \Delta T} \]

Where:
- \( Q \) is the amount of heat transferred (measured in Joules or Watts),
- \( D \) is the distance between the two isothermal planes (measured in meters),
- \( A \) is the area of the surface (measured in square meters),
- \( \Delta T \) is the temperature difference (measured in Kelvin).

### Step 1: Identify the units of each variable
- The unit of heat transferred \( Q \) is Watts (W).
- The unit of distance \( D \) is meters (m).
- The unit of area \( A \) is square meters (m²).
- The unit of temperature difference \( \Delta T \) is Kelvin (K).

### Step 2: Substitute the units into the formula
Now we substitute these units into the formula for thermal conductivity:

\[ K = \frac{Q \cdot D}{A \cdot \Delta T} \]

Substituting the units:

\[ K = \frac{W \cdot m}{m^2 \cdot K} \]

### Step 3: Simplify the expression
Now we simplify the expression:

\[ K = \frac{W \cdot m}{m^2 \cdot K} = \frac{W}{m \cdot K} \]

### Final Result
Thus, the unit of thermal conductivity \( K \) is:

\[ K = \frac{W}{m \cdot K} \]

This can also be written as:

\[ K = \text{W/m·K} \]

### Conclusion
The unit of thermal conductivity is **Watt per meter Kelvin (W/m·K)**.

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