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AP Physics 2
9.5 Specific Heat and Thermal Conductivity
AdvancedMCQMathematical25.6k
A vertical cross-sectional diagram of two stacked rectangular rock layers. The bottom layer, labeled Layer 1, has thickness L_1 and thermal conductivity k_1. The top layer, labeled Layer 2, has thickness L_2 and thermal conductivity k_2. The horizontal bottom boundary of Layer 1 is labeled with temperature T_H. The horizontal interface between Layer 1 and Layer 2 is labeled with interface temperature T_I. The horizontal top boundary of Layer 2 is labeled with temperature T_C. Vertical arrows pointing upward through the layers indicate heat flow direction. No other labels, lines, text, or axes appear.
Cross section of two rock layers undergoing steady-state heat conduction.
A section of Earth's crust consists of two flat, parallel rock layers of equal cross-sectional area \(A\). Layer 1 (bottom layer) has thickness \(L_1\) and thermal conductivity \(k_1\). Layer 2 (top layer) has thickness \(L_2\) and thermal conductivity \(k_2\). The bottom surface of Layer 1 is maintained at temperature \(T_H\) by geothermal heat, while the top surface of Layer 2 is at temperature \(T_C\), where \(T_H > T_C\). Assuming heat flows at a steady rate perpendicularly through the layers with no heat transfer through the sides, which of the following expressions represents the temperature \(T_I\) at the interface between the two rock layers?

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