---
title: "A house wall of cross-sectional area \\(A\\) and thickness \\(L\\) is made of an insulating material with thermal conductivity \\(k\\). When a temperature difference \\(\\Delta T\\) is maintained between the inner and outer surfaces of the wall, the rate of heat transfer by conduction is \\(H_0\\). A second identical layer of the same material and thickness \\(L\\) is added directly against the first wall, doubling the total thickness to \\(2L\\). If the same total temperature difference \\(\\Delta T\\) is maintained across the entire two-layer wall, what is the new rate of heat transfer through the wall?"
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url: "https://nerd-notes.com/ubq/116175/"
date_modified: "2026-08-03T11:46:08+00:00"
---

# A house wall of cross-sectional area \(A\) and thickness \(L\) is made of an insulating material with thermal conductivity \(k\). When a temperature difference \(\Delta T\) is maintained between the inner and outer surfaces of the wall, the rate of heat transfer by conduction is \(H_0\). A second identical layer of the same material and thickness \(L\) is added directly against the first wall, doubling the total thickness to \(2L\). If the same total temperature difference \(\Delta T\) is maintained across the entire two-layer wall, what is the new rate of heat transfer through the wall?

A house wall of cross-sectional area \(A\) and thickness \(L\) is made of an insulating material with thermal conductivity \(k\). When a temperature difference \(\Delta T\) is maintained between the inner and outer surfaces of the wall, the rate of heat transfer by conduction is \(H_0\). A second identical layer of the same material and thickness \(L\) is added directly against the first wall, doubling the total thickness to \(2L\). If the same total temperature difference \(\Delta T\) is maintained across the entire two-layer wall, what is the new rate of heat transfer through the wall?

![Two schematic diagrams labeled Setup 1 and Setup 2 arranged horizontally side by side. Setup 1 shows a single vertical rectangular block of thickness L and cross-sectional area A between a left wall at temperature T_1 and a right wall at temperature T_2. A horizontal arrow labeled H_0 points from left to right through the block. Setup 2 shows two identical adjacent vertical rectangular blocks, each of thickness L and thermal conductivity k, forming a combined block of total thickness 2L between the same left wall at T_1 and right wall at T_2. A horizontal arrow labeled H_new points from left to right through the combined block. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785757567-Be0Q6R.jpg)

- **A.** \(2 H_0\)
- **B.** \(H_0\)
- **C.** \(\dfrac{1}{2} H_0\)
- **D.** \(\dfrac{1}{4} H_0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116175/*