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Equivalent thermal conductivity of slabs or rods joined in series

This type of question, asked 2 times: 2021 Paper 7, 29 Jun 2022. All 2 questions below, oldest first.

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  1. Question 1

    2021 Paper 7

    6
    Two identical metal wires of thermal conductivities K1K_{1} and K2K_{2} respectively are connected in series. The effective thermal conductivity of the combination is :

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  2. Question 2

    29 Jun 2022

    23
    As per the given figure, two plates AA and BB of thermal conductivity KK and 2 K2\text{ }K are joined together to form a compound plate. The thickness of plates are 4.0 cm4.0\text{ }cm and 2.5 cm2.5\text{ }cm respectively and the area of cross-section is 120 cm2120{\text{ }cm}^{2} for each plate. The equivalent thermal conductivity of the compound plate is (1+5α)K\left( 1 +\frac{5}{\alpha} \right)K, then the value of α\alpha will be