Thermal conductivity tells you how well a material conducts heat.
Watt per meter Kelvin is a little more difficult to visualize. If you have a large window versus a small window, the large window will let more watts of heat out in the winter, right? And if it’s thinner, that will let more heat out, versus a thicker window. Also, if the temperature difference is big, more heat will be let out. So you combine all of these, and your number for thermal conductivity is in watts (energy transfer rate) per degree kelvin (difference in temperature between one side and the other) per meter (cross-sectional area of the material divided by the thickness of the material). W/mK.
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