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AP Physics 2
9.5 Specific Heat and Thermal Conductivity
AdvancedMCQMathematicalProportional Analysis16.8k
Identical conducting rods connected between thermal reservoirs in parallel and series configurations.
Identical conducting rods connected between thermal reservoirs in parallel and series configurations.
Two identical cylindrical metal rods, each of length \(L\), cross-sectional area \(A\), and thermal conductivity \(k\), connect two thermal reservoirs held at constant temperatures \(T_H\) and \(T_C\), where \(T_H > T_C\). In the parallel configuration, the two rods connect the reservoirs side-by-side; in the series configuration, the two rods are connected end-to-end to form a continuous conductor of length \(2L\) between the reservoirs. Which of the following correctly pairs the ratio of the total rate of heat conduction in parallel to that in series, \(H_{\text{parallel}} / H_{\text{series}}\), with the ratio of the magnitude of the temperature gradient in a rod in parallel to that in series, \(|\Delta T / \Delta x|_{\text{parallel}} / |\Delta T / \Delta x|_{\text{series}}\) at steady state?

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