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title: "A rigid, thermally insulated container is divided into two equal compartments by a thin partition. One compartment contains an ideal gas at an initial absolute temperature \\(T_0\\), and the other compartment is completely evacuated. The partition is suddenly removed, allowing the gas to freely expand and fill the entire container. After the system reaches a new equilibrium state, how do the final temperature \\(T_f\\) and the change in entropy of the gas \\(\\Delta S_{\\text{gas}}\\) compare to their initial states?"
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url: "https://nerd-notes.com/ubq/123044/"
date_modified: "2026-09-28T11:54:54+00:00"
---

# A rigid, thermally insulated container is divided into two equal compartments by a thin partition. One compartment contains an ideal gas at an initial absolute temperature \(T_0\), and the other compartment is completely evacuated. The partition is suddenly removed, allowing the gas to freely expand and fill the entire container. After the system reaches a new equilibrium state, how do the final temperature \(T_f\) and the change in entropy of the gas \(\Delta S_{\text{gas}}\) compare to their initial states?

A rigid, thermally insulated container is divided into two equal compartments by a thin partition. One compartment contains an ideal gas at an initial absolute temperature \(T_0\), and the other compartment is completely evacuated. The partition is suddenly removed, allowing the gas to freely expand and fill the entire container. After the system reaches a new equilibrium state, how do the final temperature \(T_f\) and the change in entropy of the gas \(\Delta S_{\text{gas}}\) compare to their initial states?

![A horizontal rectangular container with thick crosshatched walls indicating thermal insulation. A vertical thin line in the exact center divides the container into two equal left and right chambers. The left chamber contains six small solid black dots distributed throughout its volume, labeled Gas. The right chamber contains no particles and is labeled Vacuum. A dashed arrow points to the central vertical dividing line, labeled Partition. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790596493-0ma0xA.jpg)

- **A.** \(T_f < T_0\) and \(\Delta S_{\text{gas}} = 0\)
- **B.** \(T_f < T_0\) and \(\Delta S_{\text{gas}} > 0\)
- **C.** \(T_f = T_0\) and \(\Delta S_{\text{gas}} = 0\)
- **D.** \(T_f = T_0\) and \(\Delta S_{\text{gas}} > 0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123044/*