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title: "A cylindrical metal rod is thermally insulated along its sides. Its ends are maintained in contact with two large thermal reservoirs at constant absolute temperatures \\(T_H\\) and \\(T_C\\), where \\(T_H > T_C\\). The system is in a steady state, with heat conducting through the rod at a constant rate \\(P = \\dfrac{\\Delta Q}{\\Delta t}\\). Which of the following correctly identifies the rate of change of entropy of the rod, \\(\\dfrac{\\Delta S_{\\text{rod}}}{\\Delta t}\\), and the net rate of change of entropy of the complete system (the two reservoirs plus the rod), \\(\\dfrac{\\Delta S_{\\text{total}}}{\\Delta t}\\)?"
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url: "https://nerd-notes.com/ubq/122953/"
date_modified: "2026-09-28T11:54:44+00:00"
---

# A cylindrical metal rod is thermally insulated along its sides. Its ends are maintained in contact with two large thermal reservoirs at constant absolute temperatures \(T_H\) and \(T_C\), where \(T_H > T_C\). The system is in a steady state, with heat conducting through the rod at a constant rate \(P = \dfrac{\Delta Q}{\Delta t}\). Which of the following correctly identifies the rate of change of entropy of the rod, \(\dfrac{\Delta S_{\text{rod}}}{\Delta t}\), and the net rate of change of entropy of the complete system (the two reservoirs plus the rod), \(\dfrac{\Delta S_{\text{total}}}{\Delta t}\)?

A cylindrical metal rod is thermally insulated along its sides. Its ends are maintained in contact with two large thermal reservoirs at constant absolute temperatures \(T_H\) and \(T_C\), where \(T_H > T_C\). The system is in a steady state, with heat conducting through the rod at a constant rate \(P = \dfrac{\Delta Q}{\Delta t}\). Which of the following correctly identifies the rate of change of entropy of the rod, \(\dfrac{\Delta S_{\text{rod}}}{\Delta t}\), and the net rate of change of entropy of the complete system (the two reservoirs plus the rod), \(\dfrac{\Delta S_{\text{total}}}{\Delta t}\)?

![A horizontal grayscale schematic showing a rectangular metal rod centered between two large blocks. The left block is labeled Hot Reservoir, T_H. The right block is labeled Cold Reservoir, T_C. The horizontal rod connects the right edge of the left block to the left edge of the right block. A single solid horizontal arrow labeled P is centered inside the rod, pointing to the right. Hatch marks line the outer top and bottom horizontal edges of the rod. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790596484-otQUiv.jpg)

- **A.** \(\dfrac{\Delta S_{\text{rod}}}{\Delta t} = 0\) and \(\dfrac{\Delta S_{\text{total}}}{\Delta t} = P\left(\dfrac{1}{T_C} - \dfrac{1}{T_H}\right)\)
- **B.** \(\dfrac{\Delta S_{\text{rod}}}{\Delta t} = 0\) and \(\dfrac{\Delta S_{\text{total}}}{\Delta t} = 0\)
- **C.** \(\dfrac{\Delta S_{\text{rod}}}{\Delta t} = P\left(\dfrac{1}{T_C} - \dfrac{1}{T_H}\right)\) and \(\dfrac{\Delta S_{\text{total}}}{\Delta t} = 0\)
- **D.** \(\dfrac{\Delta S_{\text{rod}}}{\Delta t} = P\left(\dfrac{1}{T_H} - \dfrac{1}{T_C}\right)\) and \(\dfrac{\Delta S_{\text{total}}}{\Delta t} = P\left(\dfrac{1}{T_H} - \dfrac{1}{T_C}\right)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/122953/*