---
title: "Three heat engines, 1, 2, and 3, each operate on a Carnot cycle between a hot reservoir at absolute temperature \\(T_H\\) and a cold reservoir at absolute temperature \\(T_C\\). The operating temperatures for each engine are given in the table.  | Engine | Hot Reservoir Temperature \\(T_H\\) | Cold Reservoir Temperature \\(T_C\\) | |—|—|—| | 1 | \\(600 \\text{ K}\\) | \\(300 \\text{ K}\\) | | 2 | \\(500 \\text{ K}\\) | \\(200 \\text{ K}\\) | | 3 | \\(400 \\text{ K}\\) | \\(100 \\text{ K}\\) |  Which of the following correctly ranks the ideal thermal efficiencies \\(e_1\\), \\(e_2\\), and \\(e_3\\) of the three engines?"
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url: "https://nerd-notes.com/ubq/116158/"
date_modified: "2026-08-03T11:46:04+00:00"
---

# Three heat engines, 1, 2, and 3, each operate on a Carnot cycle between a hot reservoir at absolute temperature \(T_H\) and a cold reservoir at absolute temperature \(T_C\). The operating temperatures for each engine are given in the table.

| Engine | Hot Reservoir Temperature \(T_H\) | Cold Reservoir Temperature \(T_C\) |
|—|—|—|
| 1 | \(600 \text{ K}\) | \(300 \text{ K}\) |
| 2 | \(500 \text{ K}\) | \(200 \text{ K}\) |
| 3 | \(400 \text{ K}\) | \(100 \text{ K}\) |

Which of the following correctly ranks the ideal thermal efficiencies \(e_1\), \(e_2\), and \(e_3\) of the three engines?

Three heat engines, 1, 2, and 3, each operate on a Carnot cycle between a hot reservoir at absolute temperature \(T_H\) and a cold reservoir at absolute temperature \(T_C\). The operating temperatures for each engine are given in the table.

| Engine | Hot Reservoir Temperature \(T_H\) | Cold Reservoir Temperature \(T_C\) |
|---|---|---|
| 1 | \(600 \text{ K}\) | \(300 \text{ K}\) |
| 2 | \(500 \text{ K}\) | \(200 \text{ K}\) |
| 3 | \(400 \text{ K}\) | \(100 \text{ K}\) |

Which of the following correctly ranks the ideal thermal efficiencies \(e_1\), \(e_2\), and \(e_3\) of the three engines?

- **A.** \(e_1 > e_2 > e_3\)
- **B.** \(e_3 > e_2 > e_1\)
- **C.** \(e_1 = e_2 = e_3\)
- **D.** \(e_2 > e_3 > e_1\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116158/*