---
title: "A sealed cylinder with a movable, frictionless piston contains a fixed amount of a monatomic ideal gas. The gas is initially in state 1 at pressure \\(P_0\\), volume \\(V_0\\), and temperature \\(T_0\\). The gas can undergo two different thermodynamic processes to reach a final volume of \\(2V_0\\):  – **Process A:** The gas expands isothermally to state 2A. – **Process B:** The gas expands isobarically to state 2B."
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url: "https://nerd-notes.com/ubq/117716/"
date_modified: "2026-08-04T07:53:40+00:00"
---

# A sealed cylinder with a movable, frictionless piston contains a fixed amount of a monatomic ideal gas. The gas is initially in state 1 at pressure \(P_0\), volume \(V_0\), and temperature \(T_0\). The gas can undergo two different thermodynamic processes to reach a final volume of \(2V_0\):

– **Process A:** The gas expands isothermally to state 2A.
– **Process B:** The gas expands isobarically to state 2B.

A sealed cylinder with a movable, frictionless piston contains a fixed amount of a monatomic ideal gas. The gas is initially in state 1 at pressure \(P_0\), volume \(V_0\), and temperature \(T_0\). The gas can undergo two different thermodynamic processes to reach a final volume of \(2V_0\):

- **Process A:** The gas expands isothermally to state 2A.
- **Process B:** The gas expands isobarically to state 2B.

**Part a)** **Sketch** a graph of pressure as a function of volume for both Process A and Process B on the axes provided. **Label** the final state of Process A as 2A and the final state of Process B as 2B.

**Part b)** **Determine** the value of the ratio of the final temperature of the gas at state 2B to the final temperature of the gas at state 2A, \(T_{2B}/T_{2A}\).

**Part c)** **Indicate** whether the work done by the gas on the piston in Process A is greater than, less than, or equal to the work done by the gas in Process B. - [ ] Greater than - [ ] Less than - [ ] Equal to **Justify** your answer using features of your graph from part (a).

**Part d)** During Process B, the volume of the gas increases while the pressure remains constant. **Explain** how the gas maintains a constant pressure during this expansion. In your explanation, reference the microscopic behavior and collisions of the gas atoms with the piston.


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117716/*