---
title: "A fixed quantity of a monatomic ideal gas undergoes the cyclic process \\(1 \\to 2 \\to 3 \\to 1\\) shown in the pressure-volume diagram. Step \\(1 \\to 2\\) is an isobaric expansion at a constant pressure of \\(300 \\, \\text{kPa}\\), step \\(2 \\to 3\\) is an isochoric depressurization to \\(100 \\, \\text{kPa}\\), and step \\(3 \\to 1\\) returns the gas to state \\(1\\) along a linear path. What are the net work done **by** the gas during one complete cycle, \\(W_{\\text{net}}\\), and the thermal energy transferred **to** the gas during step \\(1 \\to 2\\), \\(Q_{12}\\)?"
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date_modified: "2026-08-21T18:57:36+00:00"
---

# A fixed quantity of a monatomic ideal gas undergoes the cyclic process \(1 \to 2 \to 3 \to 1\) shown in the pressure-volume diagram. Step \(1 \to 2\) is an isobaric expansion at a constant pressure of \(300 \, \text{kPa}\), step \(2 \to 3\) is an isochoric depressurization to \(100 \, \text{kPa}\), and step \(3 \to 1\) returns the gas to state \(1\) along a linear path. What are the net work done **by** the gas during one complete cycle, \(W_{\text{net}}\), and the thermal energy transferred **to** the gas during step \(1 \to 2\), \(Q_{12}\)?

A fixed quantity of a monatomic ideal gas undergoes the cyclic process \(1 \to 2 \to 3 \to 1\) shown in the pressure-volume diagram. Step \(1 \to 2\) is an isobaric expansion at a constant pressure of \(300 \, \text{kPa}\), step \(2 \to 3\) is an isochoric depressurization to \(100 \, \text{kPa}\), and step \(3 \to 1\) returns the gas to state \(1\) along a linear path. What are the net work done **by** the gas during one complete cycle, \(W_{\text{net}}\), and the thermal energy transferred **to** the gas during step \(1 \to 2\), \(Q_{12}\)?

![A two-dimensional Cartesian graph of pressure P in kilopascals on the vertical axis versus volume V in cubic meters multiplied by 10 to the power of negative 3 on the horizontal axis. The vertical axis has ticks labeled 100 and 300. The horizontal axis has ticks labeled 2.0 and 6.0. Three state points form a right triangle in the first quadrant: Point 1 is located at (2.0, 300), Point 2 is located at (6.0, 300), and Point 3 is located at (6.0, 100). A horizontal line with a rightward arrow connects Point 1 to Point 2. A vertical downward line with a downward arrow connects Point 2 to Point 3. A straight diagonal line with an upward-leftward arrow connects Point 3 back to Point 1, completing a clockwise triangular loop. Dashed projection lines extend from Point 1 and Point 3 to both axes. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/pv-diagram-cycle-1785826340-aEoqZ0.jpg)

- **A.** \(W_{\text{net}} = +400 \text{ J}\), \(Q_{1 \rightarrow 2} = +3000 \text{ J}\)
- **B.** \(W_{\text{net}} = +400 \text{ J}\), \(Q_{1 \rightarrow 2} = +1200 \text{ J}\)
- **C.** \(W_{\text{net}} = +800 \text{ J}\), \(Q_{1 \rightarrow 2} = +3000 \text{ J}\)
- **D.** \(W_{\text{net}} = -400 \text{ J}\), \(Q_{1 \rightarrow 2} = +1800 \text{ J}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117486/*