The dimensions of the coefficient of thermal conductivity are

$M L^{- 1} T^{- 2} K^{- 1}$

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$M L^{- 2} T^{- 3} K^{- 1}$

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

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

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Solution

The correct option is D
$M L T^{- 3} K^{- 1}$

$For bar of cross-sectional area A,length (l) and having temperatures θ_{1} and θ_{2} at its two ends, the amount of heat energy Q flowing normally across the bar in time (t) is given by Q = \frac{K A (θ 1 - θ 2) t}{l}$ $Where K is the coefficient of thermal conductivity . Therefore, K = \frac{Q l}{A (θ 1 - θ 2) t} ∴ o f k = \frac{d i m e n s i o n s o f Q \times d i m e n s i o n s o f l}{d i m e n s i o n s o f A \times o f (θ_{1} - θ_{2}) \times d i m e n s i o n s o f t} = \frac{M L^{2} T^{- 2} \times L}{L^{2} \times K \times T} = M L T^{- 3} K^{- 1}$ $Hence the correct choice is (d)$

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The dimensions of the coefficient of thermal conductivity are

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