Question

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

• A. $MLT ^{-3} K$
• B. $MLT ^{-2} K$
• C. $MLT ^{-2} K ^{-2}$
• D. $MLT ^{-3} K ^{-1}$

Answer 1

The Correct Option is D

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

Answer 2

The correct option is D)

The coefficient of thermal conductivity is 

\(K_{th} = \frac{Q\Delta X}{A\Delta Tt}\)
 

Dimensional formula of \(K_{th}\)

​[K_th]= \(\frac{[Heat].[Length]}{[Area].[Temperature].[Time]}\)

[K_th] =\(\frac{[ML^2 T^{-2}].[L]}{[L^2].[K].[T]}\)

[K_th]=[MLT⁻³K⁻¹]

The correct option is D.