First slide

Conduction

Question

Two rods with the same dimensions have thermal conductivities in the ratio 1:2. They are arranged between heat reservoirs with the same temperature difference, in two different configurations A and B. The rates of heat flow in A and B are $I_{A} and I_{B}$ respectively. The ratio $\frac{I_{A}}{I_{B}}$ is equal to

Moderate

Solution

$\begin{array}{l} Thermal current = \frac{Temperature difference}{Thermal Resistance} \\ I = \frac{ΔT}{R} \\ I n s e r i e s R_{A} = \frac{R}{2} + \frac{R}{4} = \frac{3 R}{4} \\ I n p a r a l l e l R_{B} = \frac{\frac{R}{2} . R}{\frac{R}{2} + R} = \frac{R}{3} \\ \frac{I_{A}}{I_{B}} = \frac{R_{B}}{R_{A}} = \frac{4}{9} \end{array}$

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