---
title: "A sample of an ideal gas undergoes a two-step thermodynamic process \\(1 \\rightarrow 2 \\rightarrow 3\\), as shown in the \\(PV\\) diagram. Process \\(1 \\rightarrow 2\\) is an isobaric expansion, and process \\(2 \\rightarrow 3\\) is an isochoric cooling. What is the net change in internal energy \\(\\Delta U\\) of the gas for the entire process \\(1 \\rightarrow 2 \\rightarrow 3\\)?"
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url: "https://nerd-notes.com/ubq/117395/"
date_modified: "2026-08-04T06:52:03+00:00"
---

# A sample of an ideal gas undergoes a two-step thermodynamic process \(1 \rightarrow 2 \rightarrow 3\), as shown in the \(PV\) diagram. Process \(1 \rightarrow 2\) is an isobaric expansion, and process \(2 \rightarrow 3\) is an isochoric cooling. What is the net change in internal energy \(\Delta U\) of the gas for the entire process \(1 \rightarrow 2 \rightarrow 3\)?

A sample of an ideal gas undergoes a two-step thermodynamic process \(1 \rightarrow 2 \rightarrow 3\), as shown in the \(PV\) diagram. Process \(1 \rightarrow 2\) is an isobaric expansion, and process \(2 \rightarrow 3\) is an isochoric cooling. What is the net change in internal energy \(\Delta U\) of the gas for the entire process \(1 \rightarrow 2 \rightarrow 3\)?

![A PV diagram with pressure P on the vertical axis in units of 10^5 Pa (scaled from 0 to 4) and volume V on the horizontal axis in units of 10^-3 m^3 (scaled from 0 to 8). Three states labeled 1, 2, and 3 are plotted. State 1 is at point (2, 3). State 2 is at point (6, 3). A horizontal line with an arrow pointing right connects state 1 to state 2, representing an isobaric expansion. State 3 is at point (6, 1). A vertical line with an arrow pointing downward connects state 2 to state 3, representing an isochoric cooling. Dashed projection lines connect state 1 to 2 on the V axis and 3 on the P axis; state 3 to 1 on the P axis and 6 on the V axis. Axis labels explicitly read P (10^5 Pa) and V (10^-3 m^3). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-pv-diagram-1785826322-yChaDl.jpg)

- **A.** \(-1200 \text{ J}\)
- **B.** \(-600 \text{ J}\)
- **C.** \(0 \text{ J}\)
- **D.** \(+1200 \text{ J}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117395/*