Question

What are the dimensions of the thermal conductivity coefficient \( k \) (SI units)?

• A. \( [M L^2 T^{-3} A^{-1}] \)
• B. \( [A^{-1}] \)
• C. \( [M L^2 T^{-2} A^{-1}] \)
• D. \( [L] \)

Hint:

Thermal conductivity relates heat transfer to the temperature gradient. The unit can be derived from the formula \( k = \frac{Q}{A \Delta T} \).

Answer 1

The Correct Option is C

Step 1: Understanding thermal conductivity.
Thermal conductivity \( k \) has the SI units of watts per meter-kelvin (\( \text{W}/(\text{m} \cdot \text{K}) \)), where: - \( W = \text{J/s} \), - \( J = \text{kg} \cdot \text{m}^2/\text{s}^2 \).
Step 2: Conclusion.
The dimensions of thermal conductivity \( k \) are \( [M L^2 T^{-2} A^{-1}] \), which corresponds to option (C).