SI unit of coefficient of thermal conductivity

Options

A. `Wm^(-1)K^(-1)`
B. `Wm^(-2)K^(-1)`
C. `Wm K^(-1)`
D. `Wm K^(-2 )`

Answer

To find the SI unit of the coefficient of thermal conductivity, we can follow these steps:

### Step 1: Understand the Definition
The coefficient of thermal conductivity (k) is defined as the amount of heat (Q) that passes through a unit area (A) of a material in a unit time (t) when there is a temperature difference (ΔT) of 1 Kelvin across the material.

### Step 2: Write the Formula
The formula for the coefficient of thermal conductivity can be expressed as:
\[ k = \frac{Q}{A \cdot t \cdot \Delta T} \]
Where:
- \( Q \) = Quantity of heat (in Joules)
- \( A \) = Area (in square meters)
- \( t \) = Time (in seconds)
- \( \Delta T \) = Temperature difference (in Kelvin)

### Step 3: Identify Units
Now, let's identify the units for each component in the formula:
- The unit of heat (Q) is Joules (J).
- The unit of area (A) is square meters (m²).
- The unit of time (t) is seconds (s).
- The unit of temperature difference (ΔT) is Kelvin (K).

### Step 4: Substitute the Units into the Formula
Substituting the units into the formula gives us:
\[ k = \frac{\text{J}}{\text{m}^2 \cdot \text{s} \cdot \text{K}} \]

### Step 5: Convert Joules to Watts
Since 1 Watt (W) is defined as 1 Joule per second (1 W = 1 J/s), we can rewrite the unit of heat as:
\[ \text{J} = \text{W} \cdot \text{s} \]
Substituting this into our expression for k gives:
\[ k = \frac{\text{W} \cdot \text{s}}{\text{m}^2 \cdot \text{s} \cdot \text{K}} \]

### Step 6: Simplify the Expression
The seconds (s) in the numerator and denominator cancel out:
\[ k = \frac{\text{W}}{\text{m}^2 \cdot \text{K}} \]

### Conclusion
Thus, the SI unit of the coefficient of thermal conductivity is:
\[ \text{Watt per meter square per Kelvin} \quad (\text{W/m}^2\text{K}) \]

### Final Answer
The correct option is **Watt per meter square per Kelvin (W/m²K)**.

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