---
title: "Thermodynamic Cycle — AP Physics 2 Definition & Exam Guide"
description: "A thermodynamic cycle returns a gas to its initial state, so ΔU = 0 and net heat equals net work. Learn how AP Physics 2 tests cycles on P-V diagrams."
canonical: "https://fiveable.me/ap-physics-2-revised/key-terms/thermodynamic-cycle"
type: "key-term"
subject: "AP Physics 2"
unit: "Unit 9"
---

# Thermodynamic Cycle — AP Physics 2 Definition & Exam Guide

## Definition

A thermodynamic cycle is a sequence of thermodynamic processes that returns a system to its exact initial state, so the change in internal energy over the full cycle is zero (ΔU = 0) and, by the first law, the net heat added equals the net work done by the gas. On a P-V diagram, the net work is the area enclosed by the loop.

## What It Is

A thermodynamic cycle is a chain of processes (compressions, expansions, [heating](/ap-physics-2-revised/unit-9/3-thermal-energy-transfer-and-equilibrium/study-guide/B2UC1jOK2bqVTMMH "fv-autolink"), cooling) that brings a gas right back to where it started, with the same pressure, volume, and temperature. Because [internal energy](/ap-physics-2-revised/key-terms/internal-energy "fv-autolink") is a state function (for an ideal gas, U = 3/2 nRT depends only on temperature), ending where you started means ΔU = 0 for the whole cycle. That's the move the AP exam loves.

Plug ΔU = 0 into the first law, ΔU = Q + W, and you get Q = -W. In plain terms, whatever net work the gas does on its surroundings over one cycle must be paid for by net heat flowing in. On a [P-V diagram](https://fiveable.me/key-terms/ap-physics-2-revised/p-v-diagram), a cycle shows up as a [closed loop](/ap-physics-2-revised/unit-11/6-kirchhoffs-loop-rule/study-guide/uWVN09minOrCqsRN "fv-autolink"), and the area enclosed by that loop is the net work. A clockwise loop means the gas does net positive work on its surroundings (that's an engine). Counterclockwise means net work is done on the gas.

## Why It Matters

Thermodynamic cycles live in Topic 9.4 (The First Law of Thermodynamics) in [Unit 9](/ap-physics-2-revised/unit-9 "fv-autolink"), supporting learning objectives 9.4.A (describe the internal energy of a system) and 9.4.B (describe the behavior of a system using thermodynamic processes). The cycle is where everything in Unit 9 gets stress-tested at once. You need internal energy as a [state function](/ap-physics-2-revised/key-terms/state-function "fv-autolink"), ΔU = Q + W as energy conservation, and W = -PΔV for work during volume changes, all in one problem. If you can reason through a full cycle leg by leg and check that the totals balance, you've basically proven you understand the first law instead of just memorizing it.

## Connections

### [P-V Diagram (Unit 9)](/ap-physics-2-revised/key-terms/p-v-diagram)

Cycles and P-V diagrams are inseparable on the exam. A cycle is a closed loop on the diagram, and the area trapped inside the loop is the net work per cycle. For a rectangular cycle, that area is just ΔP times ΔV, which is why scaling the width or height of the rectangle scales the work.

### [ΔU = Q + W (Unit 9)](/ap-physics-2-revised/key-terms/u-q-w)

The first law turns the cycle's ΔU = 0 into a powerful shortcut. Over one complete cycle, Q = -W, so the net heat transferred to the gas equals the net work the gas does on its surroundings. [Energy](/ap-physics-2-revised/unit-15/6-compton-scattering/study-guide/OoE2k26dtiHSsZEf "fv-autolink") in equals energy out, repeated every loop.

### [Work done by a gas (Unit 9)](/ap-physics-2-revised/key-terms/work-done-by-a-gas)

Each leg of a cycle involves work whenever [volume](/ap-physics-2-revised/unit-9/2-the-ideal-gas-law/study-guide/Nw3xH5qnLmpzH8F0 "fv-autolink") changes (W = -PΔV for work done on the gas). The signs flip between expansion and compression legs, and the leftover after everything cancels is the enclosed area. Watch the sign convention; the CED's W is work done ON the system.

### [Constant volume process (Unit 9)](/ap-physics-2-revised/key-terms/constant-volume-process)

Many exam cycles are built from simple legs like isochoric (constant volume) and isobaric (constant [pressure](/ap-physics-2-revised/unit-9/1-kinetic-theory-of-temperature-and-pressure/study-guide/wWjb2NGJDLNmMhB3 "fv-autolink")) processes. On a vertical leg of a cycle, no volume change means zero work, so all the energy transfer on that leg is heat. Recognizing which legs do zero work makes cycle problems much faster.

## On the AP Exam

Cycles show up in both multiple choice and free response. The 2021 short FRQ gave a gas taken through a cycle that included an isothermal process and asked you to reason about it leg by leg. Multiple-choice stems typically test three skills. First, geometry as work, like finding how net work changes when a rectangular cycle's width doubles and height triples (the enclosed area, ΔP·ΔV, scales by 6). Second, the first-law shortcut, recognizing that net heat per cycle equals net work W because ΔU = 0. Third, the state-function idea, such as evaluating a student's claim that ΔU over a cycle is zero (it is, because the gas returns to its initial temperature) or computing internal energy at one state from U = 3/2 nRT at another. Always start cycle problems by writing ΔU_cycle = 0, then track Q and W for each leg.

## thermodynamic cycle vs Thermodynamic process

A process is a single change between two states, like one isothermal expansion or one constant-volume heating. A cycle is a closed chain of processes that ends back at the starting state. For an individual process, ΔU is usually NOT zero. Only for the complete cycle does ΔU = 0. Mixing these up is the fastest way to lose points, so check whether the question asks about one leg or the whole loop.

## Key Takeaways

- A thermodynamic cycle returns the gas to its exact initial state, so the change in internal energy over one full cycle is zero.
- Because ΔU = 0 for a cycle, the first law (ΔU = Q + W) means the net heat added to the gas equals the net work the gas does on its surroundings.
- On a P-V diagram, the net work per cycle equals the area enclosed by the loop; for a rectangular cycle that's just ΔP times ΔV.
- A clockwise cycle on a P-V diagram does net positive work on the surroundings, while a counterclockwise cycle has net work done on the gas.
- ΔU = 0 applies to the whole cycle, not to individual legs; each leg can have its own nonzero ΔU, Q, and W that must add up correctly.
- Internal energy is a state function, so for an ideal gas U = 3/2 nRT depends only on the state, which is exactly why returning to the start makes ΔU vanish.

## FAQs

### What is a thermodynamic cycle in AP Physics 2?

It's a sequence of processes that brings a gas back to its initial pressure, volume, and temperature. Since the gas ends in its starting state, ΔU = 0 for the cycle, and the net heat added equals the net work done by the gas.

### Is the net work done in a thermodynamic cycle zero?

No. The change in internal energy is zero, but the net work is the area enclosed by the loop on the P-V diagram, which is generally nonzero. Confusing ΔU = 0 with W = 0 is one of the most common cycle mistakes on the exam.

### How is a thermodynamic cycle different from a thermodynamic process?

A process is one change between two states (one leg, like an isothermal expansion); a cycle is a closed loop of several processes that returns to the start. ΔU can be nonzero for a single process but is always zero for a complete cycle.

### How do you find the net work done in a thermodynamic cycle?

Find the area enclosed by the cycle on the P-V diagram. For a rectangular cycle, that's the width times the height, ΔP·ΔV. So doubling the width and tripling the height multiplies the net work by 6.

### What is the net heat transferred to a gas in one complete cycle?

It equals the net work the gas does on its surroundings. Since ΔU = 0 over a cycle, the first law ΔU = Q + W forces the net heat in to match the net work out, every single time the cycle repeats.

## Related Study Guides

- [9.4 The First Law of Thermodynamics](/ap-physics-2-revised/unit-9/4-the-first-law-of-thermodynamics/study-guide/MDiIPIbllDYW1klR)

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