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title: "A thermal energy of \\(600\\text{ J}\\) transfers spontaneously by conduction from a hot reservoir kept at a constant temperature of \\(400\\text{ K}\\) to a cold reservoir kept at a constant temperature of \\(300\\text{ K}\\), as shown in the diagram. Which of the following correctly compares the magnitude of the entropy change of the cold reservoir \\(|\\Delta S_{\\text{cold}}|\\) to that of the hot reservoir \\(|\\Delta S_{\\text{hot}}|\\), and states the net change in the entropy of the universe \\(\\Delta S_{\\text{univ}}\\)?"
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url: "https://nerd-notes.com/ubq/117382/"
date_modified: "2026-08-04T06:52:02+00:00"
---

# A thermal energy of \(600\text{ J}\) transfers spontaneously by conduction from a hot reservoir kept at a constant temperature of \(400\text{ K}\) to a cold reservoir kept at a constant temperature of \(300\text{ K}\), as shown in the diagram. Which of the following correctly compares the magnitude of the entropy change of the cold reservoir \(|\Delta S_{\text{cold}}|\) to that of the hot reservoir \(|\Delta S_{\text{hot}}|\), and states the net change in the entropy of the universe \(\Delta S_{\text{univ}}\)?

A thermal energy of \(600\text{ J}\) transfers spontaneously by conduction from a hot reservoir kept at a constant temperature of \(400\text{ K}\) to a cold reservoir kept at a constant temperature of \(300\text{ K}\), as shown in the diagram. Which of the following correctly compares the magnitude of the entropy change of the cold reservoir \(|\Delta S_{\text{cold}}|\) to that of the hot reservoir \(|\Delta S_{\text{hot}}|\), and states the net change in the entropy of the universe \(\Delta S_{\text{univ}}\)?

![A block diagram showing two thermal reservoirs. At the top is a rectangular box labeled 'Hot Reservoir' with text 'T_H = 400 K'. At the bottom is a rectangular box labeled 'Cold Reservoir' with text 'T_C = 300 K'. A vertical arrow points downward from the hot reservoir to the cold reservoir, labeled 'Q = 600 J'. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785826321-U9NFXf.jpg)

- **A.** \(|\Delta S_{\text{cold}}| < |\Delta S_{\text{hot}}|\) because the cold reservoir is at a lower temperature, resulting in a net entropy change of \(\Delta S_{\text{univ}} = -0.5\text{ J/K}\).
- **B.** \(|\Delta S_{\text{cold}}| > |\Delta S_{\text{hot}}|\) because the magnitude of entropy change is inversely proportional to temperature, resulting in a net entropy change of \(\Delta S_{\text{univ}} = +0.5\text{ J/K}\).
- **C.** \(|\Delta S_{\text{cold}}| = |\Delta S_{\text{hot}}|\) because equal thermal energy is transferred out of one reservoir and into the other, resulting in a net entropy change of \(\Delta S_{\text{univ}} = 0\text{ J/K}\).
- **D.** \(|\Delta S_{\text{cold}}| > |\Delta S_{\text{hot}}|\) because the cold reservoir absorbs heat at a lower temperature, but the total entropy of the universe is conserved in thermal processes, resulting in a net entropy change of \(\Delta S_{\text{univ}} = 0\text{ J/K}\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117382/*