Determining SI Unit of Thermal Conductivity

The question asks for the correct SI unit of thermal conductivity. Thermal conductivity is a measure of a material's ability to conduct heat.

Applying Fourier's Law

We can determine the unit using Fourier's Law of Heat Conduction, which relates the rate of heat transfer to the material's properties and temperature gradient. The law states:

$ \dot{Q} = -k A \frac{\Delta T}{\Delta x} $

Where:

• $ \dot{Q} $ is the rate of heat transfer (Power), measured in Watts (W).
• $ k $ is the thermal conductivity.
• $ A $ is the area perpendicular to heat flow, measured in square meters ($m^2$).
• $ \frac{\Delta T}{\Delta x} $ is the temperature gradient, measured in Kelvin per meter (K/m).

Calculating Thermal Conductivity Unit

Rearranging Fourier's Law to solve for thermal conductivity ($k$):

$ k = \frac{\dot{Q}}{-A \frac{\Delta T}{\Delta x}} $

Now, substitute the SI units of each term:

Unit of $ k = \frac{\text{Unit of } \dot{Q}}{\text{Unit of } A \times \text{Unit of } \frac{\Delta T}{\Delta x}} $

Unit of $ k = \frac{W}{m^2 \times (K/m)} $

Simplifying the expression:

Unit of $ k = \frac{W}{m^2 \cdot K / m} = \frac{W \cdot m}{m^2 \cdot K} = \frac{W}{m \cdot K} $

Conclusion on SI Unit

The SI unit for thermal conductivity ($k$) is Watts per meter-Kelvin ($W/(m \cdot K)$). Comparing this with the given options, option 3 is the correct representation.