---
title: "Constant Volume Process — AP Physics 2 Definition & Guide"
description: "A constant volume (isochoric) process locks the gas volume so W = 0 and ΔU = Q. See how it shows up on PV diagrams and first law problems in AP Physics 2 Unit 9."
canonical: "https://fiveable.me/ap-physics-2-revised/key-terms/constant-volume-process"
type: "key-term"
subject: "AP Physics 2"
unit: "Unit 9"
---

# Constant Volume Process — AP Physics 2 Definition & Guide

## Definition

A constant volume (isochoric) process is a thermodynamic process where a gas's volume stays fixed, so the gas does no work (W = -PΔV = 0) and the first law reduces to ΔU = Q. Any heat added goes entirely into internal energy, raising both temperature and pressure.

## What It Is

A constant volume process (also called an [isochoric process](/ap-physics-2-revised/key-terms/isochoric-process "fv-autolink")) is what happens when you heat or cool a gas inside a rigid, sealed container. The walls can't move, so the [volume](/ap-physics-2-revised/unit-9/2-the-ideal-gas-law/study-guide/Nw3xH5qnLmpzH8F0 "fv-autolink") never changes. Because work on a gas is defined as W = -PΔV, and ΔV = 0, no work is done on or by the gas at all.

That makes this the simplest case of [the first law of thermodynamics](/ap-physics-2-revised/unit-9/4-the-first-law-of-thermodynamics/study-guide/MDiIPIbllDYW1klR "fv-autolink"). ΔU = Q + W collapses to ΔU = Q. Every joule of heat you add becomes internal energy, and for an ideal gas, internal energy depends only on temperature (U = 3/2 nRT for a monatomic gas). So heating a gas at constant volume raises its temperature, and since the gas can't expand, the ideal gas law (PV = nRT) forces the pressure up too. On a P-V diagram, a constant volume process is a perfectly vertical line.

## Why It Matters

Constant volume processes live in Topic 9.4 (The First Law of Thermodynamics) in [Unit 9](/ap-physics-2-revised/unit-9 "fv-autolink") and directly support learning objectives 9.4.A and 9.4.B. The CED asks you to describe a system's behavior using thermodynamic processes, and the constant volume case is the cleanest one to reason through because one term in [ΔU = Q + W](/ap-physics-2-revised/key-terms/u-q-w "fv-autolink") drops out entirely.

It's also your sanity check for the work equation. W = -PΔV only produces nonzero work when volume changes, and the isochoric process is the proof. If you can explain why a rigid container means W = 0 and therefore ΔU = Q, you've shown you actually understand the first law instead of just memorizing it. That reasoning is exactly what Unit 9 questions test, whether the process appears alone or as one leg of a [thermodynamic cycle](/ap-physics-2-revised/key-terms/thermodynamic-cycle "fv-autolink").

## Connections

### ΔU = Q + W, the First Law of Thermodynamics (Unit 9)

The constant volume process is the first law with the W term deleted. Since ΔV = 0 means W = 0, you get ΔU = Q, the rare case where heat added equals [internal energy](/ap-physics-2-revised/key-terms/internal-energy "fv-autolink") gained exactly.

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

On a [P-V diagram](/ap-physics-2-revised/key-terms/p-v-diagram "fv-autolink"), constant volume means a vertical line. Heating moves you straight up (pressure rises), cooling moves you straight down. Zero area under a vertical line is the graphical proof that no work is done.

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

Cycles on the exam often include an isochoric leg. Spotting the vertical segment lets you immediately write W = 0 for that step, which simplifies the energy bookkeeping for the whole cycle.

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

A gas does work only by pushing a boundary through a volume change. A rigid container removes that option completely, so the gas can absorb heat without doing any work in return.

## On the AP Exam

Constant volume problems usually show up in multiple choice in two disguises. The first is graphical, where you're asked what a vertical line on a PV diagram means (answer: constant volume, zero work). The second is the rigid container setup, like a sealed gas heated until its pressure rises from P to 1.5P. There the volume is constant, so PV = nRT tells you temperature rises by the same factor, giving 1.5T. A third variation gives you a heater supplying energy at some rate to a gas in a rigid container; since W = 0, all of that energy becomes ΔU, and doubling the heating rate doubles the temperature change in the same time.

For free response, expect to justify your reasoning in words. A complete answer states that volume is constant, therefore W = -PΔV = 0, therefore ΔU = Q, and then connects ΔU to temperature through U = 3/2 nRT. The word "rigid" in a problem stem is your cue that this whole chain applies.

## constant volume process vs Constant pressure (isobaric) process

Both can involve heating a gas, but the geometry of the container changes everything. At constant volume (rigid container), W = 0 and all heat becomes internal energy, so the line on a P-V diagram is vertical. At constant pressure (movable piston), the gas expands and does work as it's heated, so only part of the heat raises temperature, and the P-V line is horizontal. Quick test: if heat is added and the gas does no work, it's constant volume; if the gas expands against a piston, it's constant pressure.

## Key Takeaways

- In a constant volume (isochoric) process, the volume of the gas never changes, which is what happens inside a rigid, sealed container.
- Because W = -PΔV and ΔV = 0, no work is done on or by the gas during a constant volume process.
- The first law simplifies to ΔU = Q, meaning every bit of heat added goes directly into the gas's internal energy.
- On a P-V diagram, a constant volume process is a vertical line, and the zero area under it confirms zero work.
- Since volume is fixed, the ideal gas law makes pressure and absolute temperature proportional, so a gas heated from pressure P to 1.5P ends up at temperature 1.5T.
- The word 'rigid container' in a problem is a signal to set W = 0 immediately.

## FAQs

### What is a constant volume process in AP Physics 2?

It's a thermodynamic process where a gas's volume stays fixed, like gas sealed in a rigid container. Since W = -PΔV = 0, the first law becomes ΔU = Q, so heat added equals the change in internal energy.

### Is any work done in a constant volume process?

No. Work on a gas requires a volume change (W = -PΔV), and with ΔV = 0 there is exactly zero work done on or by the gas. Graphically, the vertical line on a P-V diagram has no area under it.

### What's the difference between a constant volume process and an isothermal process?

Constant volume keeps V fixed while temperature and pressure change, so ΔU = Q. Isothermal keeps T fixed, which means ΔU = 0 for an ideal gas and Q = -W instead. They simplify the first law in completely different ways.

### What does a vertical line on a PV diagram mean?

It represents a constant volume process. Moving up the line means the gas is being heated (pressure and temperature rise), moving down means it's being cooled, and either way the work done is zero.

### If a gas in a rigid container is heated so pressure goes from P to 1.5P, what happens to the temperature?

Temperature increases to 1.5T. With volume and amount of gas constant, PV = nRT makes pressure directly proportional to absolute temperature, so multiplying P by 1.5 multiplies T by 1.5. This is a classic Unit 9 multiple choice setup.

## 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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