---
title: "A sample of an ideal gas expands from an initial state with volume \\(V_0\\) and pressure \\(P_0\\) to a final state with volume \\(2V_0\\). During this expansion, the pressure increases linearly with volume to a final pressure of \\(2P_0\\). Which of the following expressions represents the work done by the gas during this process?"
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url: "https://nerd-notes.com/ubq/116232/"
date_modified: "2026-08-21T23:32:52+00:00"
---

# A sample of an ideal gas expands from an initial state with volume \(V_0\) and pressure \(P_0\) to a final state with volume \(2V_0\). During this expansion, the pressure increases linearly with volume to a final pressure of \(2P_0\). Which of the following expressions represents the work done by the gas during this process?

A sample of an ideal gas expands from an initial state with volume \(V_0\) and pressure \(P_0\) to a final state with volume \(2V_0\). During this expansion, the pressure increases linearly with volume to a final pressure of \(2P_0\). Which of the following expressions represents the work done by the gas during this process?

![A pressure versus volume graph (P vs V) for an ideal gas expansion. The vertical axis is labeled Pressure P with tick marks labeled P_0 and 2P_0. The horizontal axis is labeled Volume V with tick marks labeled V_0 and 2V_0. State 1 is located at coordinate (V_0, P_0) and state 2 is located at coordinate (2V_0, 2P_0). A solid straight line segment with an arrowhead pointing toward state 2 connects state 1 to state 2. Dashed vertical lines extend from (V_0, P_0) down to V_0 on the volume axis and from (2V_0, 2P_0) down to 2V_0 on the volume axis. Dashed horizontal lines extend from (V_0, P_0) left to P_0 on the pressure axis and from (2V_0, 2P_0) left to 2P_0 on the pressure axis. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/fig-pv-linear-expansion-1785757584-yCgfzB.jpg)

- **A.** \(\dfrac{1}{2} P_0 V_0\)
- **B.** \(P_0 V_0\)
- **C.** \(2P_0 V_0\)
- **D.** \(\dfrac{3}{2} P_0 V_0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116232/*