Engineering
Physics
Conduction of Heat
Question
Three conducting rods of same material and cross-section are shown in figure. Temperatures of A, D and C are maintained at 20°C, 90°C and 0°C. The ratio of lengths of BD and BC if there is no heat flow in AB is:
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Solution
\[ P_{BD} = k \cdot A \cdot \frac{70}{L_{BD}}, \quad P_{BC} = k \cdot A \cdot \frac{20}{L_{BC}} \] \[ P_{BD} = P_{BC} \implies \frac{70}{L_{BD}} = \frac{20}{L_{BC}} \] \[ \frac{L_{BD}}{L_{BC}} = \boxed{\dfrac{7}{2}} \]