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title: "An ice cube at \\(0\\text{ }^\\circ\\text{C}\\) is placed into a thermally insulated container filled with warm water at \\(30\\text{ }^\\circ\\text{C}\\). The container and its contents are completely isolated from the surroundings. After some time, the ice cube melts completely and the system reaches thermal equilibrium at \\(15\\text{ }^\\circ\\text{C}\\). Which of the following correctly identifies the sign of the entropy change of the warm water, \\(\\Delta S_{\\text{water}}\\), and the sign of the total entropy change of the combined ice-water system, \\(\\Delta S_{\\text{total}}\\)?"
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url: "https://nerd-notes.com/ubq/122906/"
date_modified: "2026-09-28T11:54:35+00:00"
---

# An ice cube at \(0\text{ }^\circ\text{C}\) is placed into a thermally insulated container filled with warm water at \(30\text{ }^\circ\text{C}\). The container and its contents are completely isolated from the surroundings. After some time, the ice cube melts completely and the system reaches thermal equilibrium at \(15\text{ }^\circ\text{C}\). Which of the following correctly identifies the sign of the entropy change of the warm water, \(\Delta S_{\text{water}}\), and the sign of the total entropy change of the combined ice-water system, \(\Delta S_{\text{total}}\)?

An ice cube at \(0\text{ }^\circ\text{C}\) is placed into a thermally insulated container filled with warm water at \(30\text{ }^\circ\text{C}\). The container and its contents are completely isolated from the surroundings. After some time, the ice cube melts completely and the system reaches thermal equilibrium at \(15\text{ }^\circ\text{C}\). Which of the following correctly identifies the sign of the entropy change of the warm water, \(\Delta S_{\text{water}}\), and the sign of the total entropy change of the combined ice-water system, \(\Delta S_{\text{total}}\)?

- **A.** \(\Delta S_{\text{water}}\) is positive, and \(\Delta S_{\text{total}}\) is positive.
- **B.** \(\Delta S_{\text{water}}\) is negative, and \(\Delta S_{\text{total}}\) is positive.
- **C.** \(\Delta S_{\text{water}}\) is negative, and \(\Delta S_{\text{total}}\) is zero.
- **D.** \(\Delta S_{\text{water}}\) is positive, and \(\Delta S_{\text{total}}\) is zero.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/122906/*