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JIPMER 2015
Exam
JIPMER
Year
2015
Subject
Physics
Chapter
Thermal Properties of Matter

JIPMER 2015 · Physics · Thermal Properties of Matter

A slab consists of portions of different materials of same...

A slab consists of portions of different materials of same thickness and having the conductivities K1K_1 and K2K_2. The equivalent thermal conductivity of the slab is

Options

  1. AK1+K2K_1+K_2
  2. BK1+K2\sqrt{K_1+K_2}
  3. C2K1K2K1+K2\frac{2 K_1 K_2}{K_1+K_2}
  4. DK1K2K1+K2\sqrt{\frac{K_1 K_2}{K_1+K_2}}

Correct answer

C. 2K1K2K1+K2\frac{2 K_1 K_2}{K_1+K_2}

Step-by-step solution

As two portions of the slab are connected in series, therefore K=∑xi∑xi/K1=d+ddK1+dK2=2dd(1K1+1K2)=2K1K2K1+K2\begin{aligned} K & =\frac{\sum x_i}{\sum x_i / K_1}=\frac{d+d}{\frac{d}{K_1}+\frac{d}{K_2}} \\ & =\frac{2 d}{d\left(\frac{1}{K_1}+\frac{1}{K_2}\right)}=\frac{2 K_1 K_2}{K_1+K_2}\end{aligned}
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