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title: "Two rigid, thermally insulated compartments of equal volume \\(V\\) are connected by a closed valve. The left compartment contains \\(1.0\\text{ mol}\\) of helium gas at temperature \\(T_0\\), and the right compartment contains \\(1.0\\text{ mol}\\) of argon gas at temperature \\(T_0\\). The valve is opened, allowing the two distinct ideal gases to mix completely within the total volume \\(2V\\) while remaining thermally isolated from the environment. Which of the following correctly describes the mixing process once equilibrium is reached, along with a valid justification?"
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url: "https://nerd-notes.com/ubq/116202/"
date_modified: "2026-08-03T11:46:18+00:00"
---

# Two rigid, thermally insulated compartments of equal volume \(V\) are connected by a closed valve. The left compartment contains \(1.0\text{ mol}\) of helium gas at temperature \(T_0\), and the right compartment contains \(1.0\text{ mol}\) of argon gas at temperature \(T_0\). The valve is opened, allowing the two distinct ideal gases to mix completely within the total volume \(2V\) while remaining thermally isolated from the environment. Which of the following correctly describes the mixing process once equilibrium is reached, along with a valid justification?

Two rigid, thermally insulated compartments of equal volume \(V\) are connected by a closed valve. The left compartment contains \(1.0\text{ mol}\) of helium gas at temperature \(T_0\), and the right compartment contains \(1.0\text{ mol}\) of argon gas at temperature \(T_0\). The valve is opened, allowing the two distinct ideal gases to mix completely within the total volume \(2V\) while remaining thermally isolated from the environment. Which of the following correctly describes the mixing process once equilibrium is reached, along with a valid justification?

![A horizontal rectangular container with rigid, thermally insulated walls is divided into two equal compartments of volume V by a central vertical partition containing a closed valve. The left compartment contains Gas A (helium, 1.0 mol) at temperature T_0. The right compartment contains Gas B (argon, 1.0 mol) at temperature T_0. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785757578-MEgsw4.jpg)

- **A.** The process is reversible because no thermal energy is transferred into or out of the system (\(Q = 0\)), which means the entropy change of the system is \(\Delta S = \dfrac{Q}{T_0} = 0\).
- **B.** The process is irreversible because each gas expands into a larger total volume, increasing the number of accessible spatial microstates and resulting in a net increase in system entropy (\(\Delta S_{\text{sys}} > 0\)).
- **C.** The process is reversible because the total internal energy of the ideal gas mixture remains constant (\(\Delta U = 0\)), which requires the net change in entropy of the universe to be zero.
- **D.** The process is irreversible because thermal energy is transferred from the lighter helium atoms to the heavier argon atoms until both species reach the same root-mean-square speed.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116202/*