---
title: "A rigid cylinder is divided into two sealed compartments, A and B, by a movable, thermally conducting piston. Compartment A contains Gas A consisting of molecules with mass \\(m\\), and Compartment B contains Gas B consisting of molecules with mass \\(4m\\). After the system reaches thermal equilibrium at temperature \\(T\\), what are the ratio of the average translational kinetic energy per molecule \\(\\dfrac{K_A}{K_B}\\) and the ratio of the root-mean-square speeds \\(\\dfrac{v_{A,\\text{rms}}}{v_{B,\\text{rms}}}\\) of the gas molecules?"
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url: "https://nerd-notes.com/ubq/117391/"
date_modified: "2026-08-04T06:52:03+00:00"
---

# A rigid cylinder is divided into two sealed compartments, A and B, by a movable, thermally conducting piston. Compartment A contains Gas A consisting of molecules with mass \(m\), and Compartment B contains Gas B consisting of molecules with mass \(4m\). After the system reaches thermal equilibrium at temperature \(T\), what are the ratio of the average translational kinetic energy per molecule \(\dfrac{K_A}{K_B}\) and the ratio of the root-mean-square speeds \(\dfrac{v_{A,\text{rms}}}{v_{B,\text{rms}}}\) of the gas molecules?

A rigid cylinder is divided into two sealed compartments, A and B, by a movable, thermally conducting piston. Compartment A contains Gas A consisting of molecules with mass \(m\), and Compartment B contains Gas B consisting of molecules with mass \(4m\). After the system reaches thermal equilibrium at temperature \(T\), what are the ratio of the average translational kinetic energy per molecule \(\dfrac{K_A}{K_B}\) and the ratio of the root-mean-square speeds \(\dfrac{v_{A,\text{rms}}}{v_{B,\text{rms}}}\) of the gas molecules?

![A horizontal rectangle representing a cylinder is divided into two compartments by a vertical shaded bar representing a movable piston. The left compartment is labeled A and contains several small open circles representing gas particles of mass m. The right compartment is labeled B and contains several larger filled circles representing gas particles of mass 4m. A double-headed horizontal arrow above the piston indicates it is free to move. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785826322-5ApsSK.jpg)

- **A.** \(K_A / K_B = 1/4\)  and  \(v_{A,\text{rms}} / v_{B,\text{rms}} = 1/2\)
- **B.** \(K_A / K_B = 4\)  and  \(v_{A,\text{rms}} / v_{B,\text{rms}} = 2\)
- **C.** \(K_A / K_B = 1\)  and  \(v_{A,\text{rms}} / v_{B,\text{rms}} = 4\)
- **D.** \(K_A / K_B = 1\)  and  \(v_{A,\text{rms}} / v_{B,\text{rms}} = 2\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117391/*