Dimensional formula for thermal conductivity is (here $\mathbf{K}$ denotes the temperature):

(A) $\mathrm{MLT}^{-3} \mathrm{~K}^{-1}$

(B) $\mathrm{MLT}^{-2} \mathrm{~K}^{-2}$

(C) $\mathrm{MLT}^{-2} \mathrm{~K}$

(D) $\mathrm{MLT}^{-3} \mathrm{~K}$

JEE Main · 2020 · 04 Sep 2020 · Shift 1 · Units & Measurement

Dimensional formula for thermal conductivity is (here

K

denotes the temperature):

Answer: (A)

Thermal conductivity enters Fourier's law of heat conduction,

\frac{Q}{t} = K A \frac{Δ T}{Δ x}

, so

K = \frac{( Q / t ) Δ x}{A Δ T}

. Writing heat

Q

as energy

[M L^{2} T^{- 2}]

, the quantity

Q / t

has dimensions

[M L^{2} T^{- 3}]

; multiplying by thickness

[L]

and dividing by area

[L^{2}]

and temperature

[K]

gives

[K_{th}] = \frac{[ M L ^{2} T ^{- 3} ] [ L ]}{[ L ^{2} ] [ K ]} = M L T^{- 3} K^{- 1}

JEE Main · 2020 · 04 Sep 2020 · Shift 1 · Single correct option