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  4. Dimensional formula for thermal conductivity is (here K denotes the temperature)

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Q. Dimensional formula for thermal conductivity is (here $K$ denotes the temperature)

JEE MainJEE Main 2020Physical World, Units and Measurements

Solution:

$\because \frac{ d \theta}{ dt }= kA \frac{ dT }{ d x }$
$k =\frac{\left(\frac{ d \theta}{ dt }\right)}{ A \left(\frac{ dT }{ d x }\right)}$
$[ k ]=\frac{\left[ ML ^{2} T ^{-3}\right]}{\left[ L ^{2}\right]\left[ KL ^{-1}\right]}$
$=\left\lfloor ML T ^{-3} K ^{-1}\right\rfloor$