The unit of thermal conductivity is a crucial concept in the study of heat transfer in materials. Thermal conductivity is a measure of a material's ability to conduct heat. The standard unit of thermal conductivity is expressed in terms of watts (W), meters (m), and Kelvins (K).
Thermal conductivity (\(k\)) can be defined by the equation:
q = -k \cdot A \cdot \frac{dT}{dx}
Where:
q is the heat transfer per unit time (in watts, W).
A is the cross-sectional area through which heat is transferred (in square meters, m²).
\frac{dT}{dx} is the temperature gradient (in Kelvins per meter, K/m).
Rearranging the formula, we find that the unit of thermal conductivity is given by:
k = \frac{q}{A \cdot \frac{dT}{dx}}
This simplifies to:
k = \frac{W}{m \cdot (K/m)} = Wm^{-1}K^{-1}
Thus, the unit of thermal conductivity is Wm^{-1}K^{-1}.
Therefore, the correct answer among the given options is:
Wm^{-1}K^{-1}
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