What is the dimensional formula of thermal conductivity?

Question

What is the dimensional formula of thermal conductivity? (A) [ MLT -1 K -1] (B) [ MLT -3 K -1] (C) [ M 2 LT -3 K -2] (D) [ ML 2 T -2 K ]

Tardigrade Admin · Accepted Answer

Coefficient of thermal conductivity is K=(Δ Q × L/A(T1-T2) Δ t) Substituting dimensions for corresponding quantities in equation (i), we get [K]=([ ML 2 T -2][ L ]/[ L 2][ K ][ T ])=[ MLT -3 K -1]

Q. What is the dimensional formula of thermal conductivity?

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

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

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

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

Coefficient of thermal conductivity is
$K = \frac{Δ Q \times L}{A ( T _{1} - T _{2} ) Δ t}$
Substituting dimensions for corresponding quantities in equation (i), we get $[K] = \frac{[ M L ^{2} T ^{- 2} ] [ L ]}{[ L ^{2} ] [ K ] [ T ]} = [M L T^{- 3} K^{- 1}]$

Q. What is the dimensional formula of thermal conductivity?

[MLT−1K−1]

[MLT−3K−1]

[M2LT−3K−2]

[ML2T−2K]

Coefficient of thermal conductivity is K=A(T1​−T2​)ΔtΔQ×L​ Substituting dimensions for corresponding quantities in equation (i), we get [K]=[L2][K][T][ML2T−2][L]​=[MLT−3K−1]

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

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

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

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

Coefficient of thermal conductivity is
$K = \frac{Δ Q \times L}{A ( T _{1} - T _{2} ) Δ t}$
Substituting dimensions for corresponding quantities in equation (i), we get $[K] = \frac{[ M L ^{2} T ^{- 2} ] [ L ]}{[ L ^{2} ] [ K ] [ T ]} = [M L T^{- 3} K^{- 1}]$