As per the given figure, two plates A and B of thermal conductivity K… | JEE Main 2022 (29 Jun, Shift 1)

Q30JEE Main 2022 · 29 JUN · SHIFT 1Medium

Heat Conduction

As per the given figure, two plates A and B of thermal conductivity K and 2 K are joined together to form a compound plate. The thickness of plates are 4.0 cm and 2.5 cm respectively and the area of cross-section is 120 cm2 for each plate. The equivalent thermal conductivity of the compound plate is $\left(1 + \frac{5}{\alpha}\right)$ K, then the value of $\alpha$ will be ______________.

Numerical answer type. Work it out, then open the answer.

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Answer: 21

Plates in series: $\dfrac{L_1+L_2}{K_{eq}} = \dfrac{L_1}{K_1} + \dfrac{L_2}{K_2}$
$\dfrac{6.5}{K_{eq}} = \dfrac{4}{K} + \dfrac{2.5}{2K} = \dfrac{5.25}{K} \Rightarrow K_{eq} = \dfrac{6.5}{5.25}K = \dfrac{26}{21}K$
$\dfrac{26}{21} = 1 + \dfrac{5}{21}$
So $\alpha = 21$

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