A slab consists of two layers of different materials of the same thickness and having thermal conductivities K1 and K2 are connected in series. The equivalent thermal conductivity of the slab is

Question

A slab consists of two layers of different materials of the same thickness and having thermal conductivities K1 and K2 are connected in series. The equivalent thermal conductivity of the slab is (A) (2K1K2/K1+K2) (B) √K1K2 (C) (K1K2/K1+K2) (D) K1+K2

Tardigrade Admin · Accepted Answer

In series combination, (t/K1)+(t/K2)=(2t/K) ⇒ (1/K1)+(1/K2)=(2/K) ⇒ K=(2K1K2/K1+K2).

Q. A slab consists of two layers of different materials of the same thickness and having thermal conductivities $K_{1}$ and $K_{2}$ are connected in series. The equivalent thermal conductivity of the slab is

$\frac{2 K _{1} K _{2}}{K _{1} + K _{2}}$

$K_{1} K_{2}$

$\frac{K _{1} K _{2}}{K _{1} + K _{2}}$

$K_{1} + K_{2}$

In series combination, $\frac{t}{K _{1}} + \frac{t}{K _{2}} = \frac{2 t}{K}$
$\Rightarrow \frac{1}{K _{1}} + \frac{1}{K _{2}} = \frac{2}{K}$
$\Rightarrow K = \frac{2 K _{1} K _{2}}{K _{1} + K _{2}}$ .

Q. A slab consists of two layers of different materials of the same thickness and having thermal conductivities K1​ and K2​ are connected in series. The equivalent thermal conductivity of the slab is

K1​+K2​2K1​K2​​

K1​K2​​

K1​+K2​K1​K2​​

K1​+K2​