---
title: "A sample of a monatomic ideal gas undergoes the three-step cyclic process \\(1 \\rightarrow 2 \\rightarrow 3 \\rightarrow 1\\) shown in the \\(PV\\) diagram. Process \\(1 \\rightarrow 2\\) is an isobaric expansion at a pressure of \\(2.0 \\times 10^5 \\text{ Pa}\\) from an initial volume of \\(1.0 \\times 10^{-3} \\text{ m}^3\\) to a final volume of \\(4.0 \\times 10^{-3} \\text{ m}^3\\). Process \\(2 \\rightarrow 3\\) is an isochoric pressure decrease, and process \\(3 \\rightarrow 1\\) is an adiabatic compression during which \\(300 \\text{ J}\\) of work is done on the gas. What is the thermal efficiency of this cycle?"
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url: "https://nerd-notes.com/ubq/116276/"
date_modified: "2026-08-03T11:46:35+00:00"
---

# A sample of a monatomic ideal gas undergoes the three-step cyclic process \(1 \rightarrow 2 \rightarrow 3 \rightarrow 1\) shown in the \(PV\) diagram. Process \(1 \rightarrow 2\) is an isobaric expansion at a pressure of \(2.0 \times 10^5 \text{ Pa}\) from an initial volume of \(1.0 \times 10^{-3} \text{ m}^3\) to a final volume of \(4.0 \times 10^{-3} \text{ m}^3\). Process \(2 \rightarrow 3\) is an isochoric pressure decrease, and process \(3 \rightarrow 1\) is an adiabatic compression during which \(300 \text{ J}\) of work is done on the gas. What is the thermal efficiency of this cycle?

A sample of a monatomic ideal gas undergoes the three-step cyclic process \(1 \rightarrow 2 \rightarrow 3 \rightarrow 1\) shown in the \(PV\) diagram. Process \(1 \rightarrow 2\) is an isobaric expansion at a pressure of \(2.0 \times 10^5 \text{ Pa}\) from an initial volume of \(1.0 \times 10^{-3} \text{ m}^3\) to a final volume of \(4.0 \times 10^{-3} \text{ m}^3\). Process \(2 \rightarrow 3\) is an isochoric pressure decrease, and process \(3 \rightarrow 1\) is an adiabatic compression during which \(300 \text{ J}\) of work is done on the gas. What is the thermal efficiency of this cycle?

![A pressure versus volume graph (PV diagram) displaying a closed three-step thermodynamic cycle labeled 1, 2, and 3. The vertical axis is labeled Pressure P in 10^5 Pa with tick marks at 1.0 and 2.0. The horizontal axis is labeled Volume V in 10^-3 m^3 with tick marks at 1.0 and 4.0. State 1 is located at (1.0, 2.0). A horizontal line with an arrow pointing right connects state 1 to state 2 at (4.0, 2.0), representing an isobaric expansion. A vertical dashed line with an arrow pointing down connects state 2 to state 3 at (4.0, 1.0), representing an isochoric pressure drop. A smooth curve convex downward with an arrow pointing up-left connects state 3 back to state 1, representing an adiabatic compression. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785757594-5Kt8Sx.jpg)

- **A.** \(10\%\)
- **B.** \(20\%\)
- **C.** \(40\%\)
- **D.** \(50\%\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116276/*