Dimensional formula for thermal conductivity is (here $K$ denotes the temperature :
Question:

Dimensional formula for thermal conductivity is (here $K$ denotes the temperature :

  1. $\mathrm{MLT}^{-2} \mathrm{~K}$

  2. $\mathrm{MLT}^{-2} \mathrm{~K}^{-2}$

  3. $\mathrm{MLT}^{-3} \mathrm{~K}$

  4. $\mathrm{MLT}^{-3} \mathrm{~K}^{-1}$


Correct Option: , 4

Solution:

(4) From formula, $\frac{d Q}{d t}=k A \frac{d T}{d x}$

$\Rightarrow k=\frac{\left(\frac{d Q}{d t}\right)}{A\left(\frac{d T}{d x}\right)}$

$[k]=\frac{\left[\mathrm{ML}^{2} \mathrm{~T}^{-3}\right]}{\left[\mathrm{L}^{2}\right]\left[\mathrm{KL}^{-1}\right]}=\left[\mathrm{MLT}^{-3} \mathrm{~K}^{-1}\right]$

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