---
title: "A composite rod consists of two cylindrical segments, Segment 1 and Segment 2, made of the same uniform material. Both segments have length \\(L\\), but Segment 1 has cross-sectional area \\(A\\) while Segment 2 has cross-sectional area \\(2A\\). The rod is connected between a hot reservoir at temperature \\(T_H\\) and a cold reservoir at temperature \\(T_C\\), and its outer surfaces are thermally insulated. Once the system reaches steady state, how do the heat transfer rate \\(H_1\\) through Segment 1 and the temperature difference \\(\\Delta T_1\\) across Segment 1 compare to the heat transfer rate \\(H_2\\) through Segment 2 and the temperature difference \\(\\Delta T_2\\) across Segment 2?"
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url: "https://nerd-notes.com/ubq/116230/"
date_modified: "2026-08-03T11:46:24+00:00"
---

# A composite rod consists of two cylindrical segments, Segment 1 and Segment 2, made of the same uniform material. Both segments have length \(L\), but Segment 1 has cross-sectional area \(A\) while Segment 2 has cross-sectional area \(2A\). The rod is connected between a hot reservoir at temperature \(T_H\) and a cold reservoir at temperature \(T_C\), and its outer surfaces are thermally insulated. Once the system reaches steady state, how do the heat transfer rate \(H_1\) through Segment 1 and the temperature difference \(\Delta T_1\) across Segment 1 compare to the heat transfer rate \(H_2\) through Segment 2 and the temperature difference \(\Delta T_2\) across Segment 2?

A composite rod consists of two cylindrical segments, Segment 1 and Segment 2, made of the same uniform material. Both segments have length \(L\), but Segment 1 has cross-sectional area \(A\) while Segment 2 has cross-sectional area \(2A\). The rod is connected between a hot reservoir at temperature \(T_H\) and a cold reservoir at temperature \(T_C\), and its outer surfaces are thermally insulated. Once the system reaches steady state, how do the heat transfer rate \(H_1\) through Segment 1 and the temperature difference \(\Delta T_1\) across Segment 1 compare to the heat transfer rate \(H_2\) through Segment 2 and the temperature difference \(\Delta T_2\) across Segment 2?

![A horizontal composite cylindrical rod connected between two large rectangular thermal reservoirs. On the left is a hot reservoir labeled T_H. Attached to it is Segment 1, a horizontal cylinder of length L and cross-sectional area A. Attached coaxially to the right end of Segment 1 is Segment 2, a horizontal cylinder of the same length L but with a larger cross-sectional area 2A. The right end of Segment 2 attaches to a cold reservoir labeled T_C. The outer curved boundaries of both cylindrical segments feature diagonal hatching lines to represent thermal insulation. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785757584-9XXk1X.jpg)

- **A.** \(H_1 = 2H_2\) and \(\Delta T_1 = \Delta T_2\)
- **B.** \(H_1 = \dfrac{1}{2}H_2\) and \(\Delta T_1 = 2\Delta T_2\)
- **C.** \(H_1 = H_2\) and \(\Delta T_1 = 2\Delta T_2\)
- **D.** \(H_1 = H_2\) and \(\Delta T_1 = \dfrac{1}{2}\Delta T_2\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116230/*