JEE Mains · Physics · STD 11 - 10.2 transmission of heat
A cylinder of radius \(R\) is surrounded by a cylindrical shell of inner radius \(R\) and outer radius \(2R\). The thermal conductivity of the material of the inner cylinder is \(K_1\) and that of the outer cylinder is \(K_2\). Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is
- A \(\frac{{{K_1} + {K_2}}}{2}\)
- B \(K_1 + K_2\)
- C \(\frac{{2{K_1} + {3K_2}}}{5}\)
- D \(\frac{{{K_1} + {3K_2}}}{4}\)
Answer & Solution
Correct Answer
(D) \(\frac{{{K_1} + {3K_2}}}{4}\)
Step-by-step Solution
Detailed explanation
Equivalent thermal resisitance, \(\frac{1}{R} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}}\) \(\frac{{k\pi {{\left( {2R} \right)}^2}}}{L} = \frac{{{k_1}\pi {R^2}}}{L} + \frac{{{k_2}\pi \left[ {{{\left( {2R} \right)}^2} - {R^2}} \right]}}{L}\) \( \Rightarrow 4k = {k_1} + 3{k_2}\)…
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