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 determine the unit of thermal conductivity, we start with the definition of thermal conductivity (k). Thermal conductivity is defined as the amount of heat (Q) that passes through a material per unit time (t), per unit area (A), and per unit temperature difference (ΔT) across a length (L). The formula can be expressed as:

\[ Q = k \cdot A \cdot \frac{(T_2 - T_1)}{L} \]

Where:
- \( Q \) = heat transfer (in Joules or Watts)
- \( k \) = thermal conductivity (in Watts per meter per Kelvin)
- \( A \) = area (in square meters)
- \( T_2 - T_1 \) = temperature difference (in Kelvin)
- \( L \) = thickness or length (in meters)

We can rearrange the formula to solve for thermal conductivity \( k \):

\[ k = \frac{Q \cdot L}{A \cdot (T_2 - T_1)} \]

Now, let's analyze the units involved in this equation:

1. **Units of Heat (Q)**: The unit of heat is Joules (J), which is equivalent to Watts (W) when considering the rate of heat transfer (1 W = 1 J/s).
2. **Units of Length (L)**: The unit of length is meters (m).
3. **Units of Area (A)**: The unit of area is square meters (m²).
4. **Units of Temperature Difference (ΔT)**: The unit of temperature difference is Kelvin (K).

Now, substituting these units into the equation for thermal conductivity:

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

This simplifies to:

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

Thus, the unit of thermal conductivity is:

\[ \text{Watt per meter per Kelvin} \quad \text{(W/m·K)} \]

Therefore, the correct answer to the question is:

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

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