---
title: "A solid metal rod of length \\(L\\) and cross-sectional area \\(A\\) conducts energy at a steady rate \\(P_0\\) between two thermal reservoirs maintained at constant temperatures \\(T_H\\) and \\(T_C\\), with \\(T_H > T_C\\). A second rod, made of the same metal, has a length of \\(2L\\) and a cross-sectional area of \\(2A\\). If the second rod is connected between the same two thermal reservoirs, what is the rate of energy transfer through the second rod?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/116159/"
date_modified: "2026-08-03T11:46:04+00:00"
---

# A solid metal rod of length \(L\) and cross-sectional area \(A\) conducts energy at a steady rate \(P_0\) between two thermal reservoirs maintained at constant temperatures \(T_H\) and \(T_C\), with \(T_H > T_C\). A second rod, made of the same metal, has a length of \(2L\) and a cross-sectional area of \(2A\). If the second rod is connected between the same two thermal reservoirs, what is the rate of energy transfer through the second rod?

A solid metal rod of length \(L\) and cross-sectional area \(A\) conducts energy at a steady rate \(P_0\) between two thermal reservoirs maintained at constant temperatures \(T_H\) and \(T_C\), with \(T_H > T_C\). A second rod, made of the same metal, has a length of \(2L\) and a cross-sectional area of \(2A\). If the second rod is connected between the same two thermal reservoirs, what is the rate of energy transfer through the second rod?

![A schematic diagram showing two thermal conduction setups labeled Rod 1 and Rod 2, positioned vertically one above the other. On the left of both setups is a red rectangular block labeled T_H, representing a hot reservoir. On the right of both setups is a blue rectangular block labeled T_C, representing a cold reservoir. Setup 1 shows Rod 1, a grey horizontal cylinder of length L and cross-sectional area A connecting the two reservoirs. Setup 2 shows Rod 2, a wider and longer grey horizontal cylinder of length 2L and cross-sectional area 2A connecting identical T_H and T_C reservoirs. Double-headed dimension arrows indicate length L for Rod 1 and length 2L for Rod 2. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785757564-cuGkrf.jpg)

- **A.** \(P_0\)
- **B.** \(2P_0\)
- **C.** \(4P_0\)
- **D.** \(\dfrac{1}{2}P_0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116159/*