---
title: "Work Done by a Gas — AP Physics 2 Definition & Guide"
description: "Work done by a gas is energy a gas transfers as it expands against external pressure. Learn the sign convention, P-V diagram area, and first law on AP Physics 2."
canonical: "https://fiveable.me/ap-physics-2-revised/key-terms/work-done-by-a-gas"
type: "key-term"
subject: "AP Physics 2"
unit: "Unit 9"
---

# Work Done by a Gas — AP Physics 2 Definition & Guide

## Definition

Work done by a gas is the energy a gas transfers to its surroundings as it changes volume against external pressure. It's positive when the gas expands and negative when it's compressed, and it equals the area under the process curve on a P-V diagram. It's the opposite sign of work done ON the gas (W = −PΔV).

## What It Is

When a gas expands inside a container, it pushes on whatever is holding it in (like a piston) and transfers [energy](/ap-physics-2-revised/unit-15/6-compton-scattering/study-guide/OoE2k26dtiHSsZEf "fv-autolink") out of the system. That energy transfer is the work done by the gas. When the gas gets squeezed instead, the surroundings do work on the gas, so the work done by the gas comes out negative.

Here's the part that trips everyone up. The [AP Physics 2](/ap-physics-2-revised "fv-autolink") CED writes the first law as [ΔU = Q + W](/ap-physics-2-revised/key-terms/u-q-w "fv-autolink"), where W is the work done **on** the system, defined as W = −PΔV for a constant or average external pressure. Work done **by** the gas is just the negative of that, so W(by gas) = +PΔV. Expansion means ΔV is positive, so the gas does positive work on its surroundings, and that energy leaves the system. Compression means ΔV is negative, so the work done by the gas is negative (really, work is being done on it). On a P-V diagram, the magnitude of this work is the area under the process curve. Same physics either way; the sign convention just depends on whose perspective you're taking.

## Why It Matters

This concept lives in Topic 9.4 (The First Law of Thermodynamics) in [Unit 9](/ap-physics-2-revised/unit-9 "fv-autolink") and directly supports learning objectives 9.4.A and 9.4.B. The first law, ΔU = Q + W, is [conservation of energy](/ap-physics-2-revised/key-terms/conservation-of-energy "fv-autolink") with a thermodynamics accent. To use it, you have to correctly account for the work term, and that means knowing instantly whether the gas is gaining or losing energy through volume change. If a gas expands, it does work on the surroundings and its internal energy drops (unless heat flows in to compensate). For an ideal monatomic gas, internal energy is U = 3/2 nRT, so any work the gas does without heat input shows up as a temperature drop. Almost every Unit 9 problem, from isothermal expansions to full heat-engine cycles, hinges on getting this work term and its sign right.

## Connections

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

These are two views of the same [energy transfer](/ap-physics-2-revised/unit-11/4-electric-power/study-guide/XlqNl6VwuwtsWe2m "fv-autolink"). The CED equation W = −PΔV gives work done ON the gas, and work done BY the gas is just its negative. If the gas does +500 J of work expanding, then −500 J of work was done on it. Pick one perspective per problem and stay consistent.

### ΔU = Q + W, the first law (Unit 9)

Work is one of only two ways energy crosses the boundary of a [closed system](/ap-physics-2-revised/key-terms/closed-system "fv-autolink") (heating is the other). When a gas expands and does work, that energy has to come from somewhere, either from heat flowing in or from the gas's own internal energy dropping.

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

The area under a process curve on a [pressure-volume graph](/ap-physics-2-revised/key-terms/pressure-volume-graph "fv-autolink") equals the magnitude of the work. Direction matters too. Moving rightward (expansion) means the gas does positive work; moving leftward (compression) means negative work by the gas.

### [Thermodynamic cycle (Unit 9)](/ap-physics-2-revised/key-terms/thermodynamic-cycle)

In a complete cycle, the net work done by the gas equals the area enclosed by the loop on the P-V diagram. Clockwise loops mean the gas does net positive work, which is exactly how a heat engine converts heat into useful work.

## On the AP Exam

No released FRQ in the revised course has used the phrase 'work done by a gas' verbatim, but the underlying skill shows up constantly in Unit 9 questions. Multiple-choice stems give you a P-V diagram and ask you to rank the work done in different processes, identify its sign, or compare it to the heat added using ΔU = Q + W. FRQs ask you to calculate work as the area under a P-V curve, explain why an expanding gas cools when no heat is added, or analyze the net work in a cycle. The single biggest point-loser is the sign convention. Read the question carefully to see whether it asks for work done ON the gas or BY the gas, because they differ by a minus sign, and justify your answer in terms of energy entering or leaving the system.

## Work done by a gas vs Work done on a system

They're equal in magnitude and opposite in sign. The AP Physics 2 equation sheet gives W = −PΔV, which is the work done ON the gas, and that's the W that goes into ΔU = Q + W. Work done BY the gas is +PΔV. So when a gas expands (ΔV > 0), the gas does positive work on the surroundings, but the W in the first law is negative because energy is leaving the system. If your internal energy change has the wrong sign, this swap is almost always the culprit.

## Key Takeaways

- Work done by a gas is positive when the gas expands and negative when the gas is compressed.
- The AP equation W = −PΔV gives work done ON the gas, so work done BY the gas is +PΔV, the opposite sign.
- On a P-V diagram, the magnitude of the work equals the area under the process curve, and for a full cycle the net work by the gas equals the enclosed area.
- At constant volume (ΔV = 0), the gas does zero work no matter how much the pressure changes.
- By the first law, ΔU = Q + W, a gas that expands without heat input must lose internal energy, which means its temperature drops since U = 3/2 nRT for an ideal monatomic gas.
- W = −PΔV only works directly when external pressure is constant or you use an average; otherwise you need the area under the P-V curve.

## FAQs

### What is work done by a gas in AP Physics 2?

It's the energy a gas transfers to its surroundings as it changes volume against external pressure. It equals +PΔV for constant pressure (positive for expansion, negative for compression) and equals the area under the curve on a P-V diagram.

### Is work done by a gas the same as W in ΔU = Q + W?

No. In the AP Physics 2 CED, the W in ΔU = Q + W is work done ON the system, given by W = −PΔV. Work done BY the gas is the negative of that. If the gas does 200 J of work expanding, you plug W = −200 J into the first law.

### Does a gas do work if its volume doesn't change?

No. Work requires a volume change, so in a constant volume (isochoric) process the gas does zero work even if its pressure and temperature change a lot. Any internal energy change in that case comes entirely from heating or cooling (ΔU = Q).

### How do I find work done by a gas from a P-V diagram?

Take the area under the process curve between the initial and final volumes. The work is positive if the gas moves to larger volume (expansion) and negative if it moves to smaller volume. For a complete cycle, the net work done by the gas is the area enclosed by the loop, positive for a clockwise cycle.

### Why does a gas cool down when it expands?

An expanding gas does positive work on its surroundings, and that energy has to come from somewhere. If no heat flows in, the gas's internal energy drops, and since U = 3/2 nRT for an ideal monatomic gas, lower internal energy means lower temperature.

## 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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