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For what stands gm. The calculation is correct. gm is already in K.The unit in SI is W/(mK) means Watt devided by meter and Kelvin ( Temperatur). Could be gm also a length?

But a thermal conductivity has nothing to do with a mass. If it has a value of 1 W/mK then it doesn't matter you have 1 g or 1 kg of it. The conductivity is the same. Its like electrical conductivity. It's only depending on length, thickness and type of material.