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 \(\;\frac{{{K_1}{K_2}}}{{2({K_1} + {K_2})}}\)
D \(\;\frac{{{K_1} + {K_2}}}{2}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\;\frac{{{K_1} + {K_2}}}{2}\)

Step-by-step Solution

Detailed explanation

In parallel \(K_{eq}=\frac{ K _{1} A _{1}+ K _{2} A _{2}}{ A _{1}+ A _{2}}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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