First slide

Dimensions of physical quantities

Question

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

Moderate

A

$M L T^{- 2} K^{- 2}$
B

$M L T^{- 3} K^{- 1}$
C

$M L T^{- 2} K$
D

$M L T^{- 3} K$

Solution

Rate of heat flow in steady state in the process of conduction is given by
$\begin{array}{l} \frac{d Q}{d t} = \frac{k A Δ T}{Δ x} \\ \Rightarrow k = \frac{(\frac{d Q}{d t}) (Δ x)}{(Δ T) A} \\ \Rightarrow [k] = \frac{(work)}{(Time) (Temp) (length)} \\ = \frac{Force}{(Time) (Temp)} = \frac{[{MLT}^{- 2}]}{T K} = [ML T^{- 3} K^{- 1}] \end{array}$

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