A wall consists of alternating blocks of length d and coefficient… - Vidyadip

MCQ

A wall consists of alternating blocks of length $d$ and coefficient of thermal conductivity $K_{1}$ and $K_{2}$ respectively as shown in figure. The cross sectional area of the blocks are the same. The equivalent coefficient of thermal conductivity of the wall between left and right is

A
$\frac{{2{K_1}{K_2}}}{{{K_1} + {K_2}}}$
B
$\frac{{{K_1} + {K_2}}}{3}$
C
$\;\frac{{{K_1}{K_2}}}{{2({K_1} + {K_2})}}$
✓
$\;\frac{{{K_1} + {K_2}}}{2}$

✓

Answer

Correct option: D.

$\;\frac{{{K_1} + {K_2}}}{2}$

d
In parallel

$K_{eq}=\frac{ K _{1} A _{1}+ K _{2} A _{2}}{ A _{1}+ A _{2}}$

Cross sectional Area $A _{1}= A _{2}= A$, for all rods.

for any two rods having same coefficient, $K _{1}$ the resultant is also $K _{1}$

so the above combination will reduce to a combination having just two rods one with $K _{1}$ and another with $K _{2}$

So net coefficient of conductivity will be $K=\frac{K_{1}+K_{2}}{2}$

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