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COMEDK · Physics · 12. Thermal Properties of Matter

A cylinder of radius \(r\) and of thermal conductivity \(K_1\) is surrounded by a cylindrical shell of inner radius \(r\) and outer radius \(2 r\) made of a material of thermal conductivity \(K_2\). The effective thermal conductivity of the system is

  1. A \(\frac{1}{3}\left(K_1+2 K_2\right)\)
  2. B \(\frac{1}{3}\left(3 K_2+2 K_1\right)\)
  3. C \(\frac{1}{3}\left(3 K_2+2 K_1\right)\)
  4. D \(\frac{1}{4}\left(K_1+3 K_2\right)\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{1}{4}\left(K_1+3 K_2\right)\)

Step-by-step Solution

Detailed explanation

Both the cylinders are in parallel, for the heat flow from one end as shown So, \(K_{\mathrm{eq}}=\frac{K_1 A_1+K_2 A_2}{A_1+A_2}\) where, \(A_1=\) area of cross-section of inner cylinder \(=\pi R^2\) and \(\quad A_2=\) area of cross-section of cylindrical shell…