---
title: "A sample of an ideal gas is contained within a vertical cylinder sealed at the top by a frictionless piston of mass \\(m\\) that is free to move. Initially, the gas has an absolute temperature \\(T_0\\) and occupies a volume \\(V_0\\). Heat is slowly removed from the gas, causing its absolute temperature to decrease to \\(\\dfrac{1}{3}T_0\\) while the atmospheric pressure outside the cylinder remains constant. What is the final volume of the gas in terms of \\(V_0\\)?"
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url: "https://nerd-notes.com/ubq/116166/"
date_modified: "2026-08-03T11:46:06+00:00"
---

# A sample of an ideal gas is contained within a vertical cylinder sealed at the top by a frictionless piston of mass \(m\) that is free to move. Initially, the gas has an absolute temperature \(T_0\) and occupies a volume \(V_0\). Heat is slowly removed from the gas, causing its absolute temperature to decrease to \(\dfrac{1}{3}T_0\) while the atmospheric pressure outside the cylinder remains constant. What is the final volume of the gas in terms of \(V_0\)?

A sample of an ideal gas is contained within a vertical cylinder sealed at the top by a frictionless piston of mass \(m\) that is free to move. Initially, the gas has an absolute temperature \(T_0\) and occupies a volume \(V_0\). Heat is slowly removed from the gas, causing its absolute temperature to decrease to \(\dfrac{1}{3}T_0\) while the atmospheric pressure outside the cylinder remains constant. What is the final volume of the gas in terms of \(V_0\)?

![A vertical cylindrical container sealed at the top by a horizontal, weighted piston of mass m. Inside the cylinder, ideal gas particles fill a region of height representing initial volume V_0. Vertical arrows pointing down on top of the piston represent constant atmospheric pressure P_atm. A horizontal arrow pointing left away from the lower cylinder wall indicates heat energy leaving the gas. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785757566-x5qfZc.jpg)

- **A.** \(\dfrac{1}{9}V_0\)
- **B.** \(\dfrac{1}{3}V_0\)
- **C.** \(3V_0\)
- **D.** \(9V_0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116166/*