Physics · Article

Physical systems, states, boundaries, and environments

Choose what belongs to an investigation, describe its condition at a stated time, and identify interactions with what lies outside its boundary.

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After reading, you can

Choose a physical system that fits a question and state what it includes.
Distinguish a system, its boundary and its surroundings.
Explain why a state description needs the variables required by the chosen model.
Identify an interaction as internal or across a boundary for a stated system.
Distinguish open, closed and isolated systems in the thermodynamic sense.

Begin with the question and choose a system

Suppose water is cooling in a cup. You could investigate the water, the water together with the cup, or a larger region that includes nearby air. Each choice asks you to include different things. A physical system is the part of the physical situation selected for study: an object, a collection of objects or a specified region.

A system choice defines the subject of your model. It does not alter the physical situation. State what belongs inside, and choose the system that makes your question clear. Several choices can describe the same event; they require different accounts of its interactions.

State where the system ends

The system boundary separates what you include from its surroundings, also called its environment. A boundary may follow a material surface or be an imagined surface around a region. It may move. Drawing it does not create a wall or prevent a real interaction.

For a system consisting of the water alone, the cup and air are outside. For water plus cup, the cup is inside and the air remains outside. Describe the selected boundary before deciding which interactions cross it. Objects outside the system can still affect it.

Describe the state at the resolution your model needs

A state describes a system's condition at a stated time using the properties required by a model. In equilibrium thermodynamics, an adequate set of macroscopic properties determines the other thermodynamic properties within that description. Temperature, pressure, volume and composition can matter. These variables do not list every molecule's position.

For simple motion along a track, position alone does not tell you which way a cart is moving. Include velocity and the position reference. For nonuniform water, one temperature cannot describe every location; a useful model may require several local temperatures. The state description must fit the question and its assumptions.

State here means condition. It is broader than the phase labels solid, liquid and gas. Two samples can both be liquid while having different temperatures. Selecting only the variables you have measured does not guarantee that you have enough information to predict a change.

Follow interactions across the chosen boundary

Ask whether matter enters or leaves and how energy is transferred. Energy can cross a boundary through heating or work, including mechanical or electrical interactions; moving matter can also carry energy. In thermodynamics, heat names energy transfer due to a temperature difference.

When warmer water transfers energy to a cooler cup, that transfer crosses the boundary of the water-only system. For water plus cup, it occurs internally. Energy transfer between either part and the outside air still crosses the larger boundary. Changing the system changes this classification, while the physical transfer remains the same.

Distinguish open, closed and isolated systems

In thermodynamics, these labels describe exchanges across a stated boundary. A closed system admits no matter exchange but can exchange energy. An open system admits matter exchange, with energy carried by that matter or transferred in other ways. An isolated system exchanges neither matter nor energy with its surroundings.

A sealed vessel can warm, so closed does not mean unchanging. No heat transfer, called an adiabatic condition, also does not guarantee isolation: work may still transfer energy. Apply a real isolation approximation only for an interval and accuracy where neglected exchanges are small enough for the question.

Thermodynamic classification for a specified boundary
System type	Matter exchange	Energy exchange
Open	Allowed	Allowed
Closed	Excluded	Allowed
Isolated	Excluded	Excluded

Make the system description useful for a prediction

Write down the question, included objects or region, boundary, observation time, state variables and relevant surroundings. Identify which interactions are included and which are neglected. A prediction then needs a model of how the state changes under those interactions; naming a system alone supplies no law of change.

Check the result against observations of the specified quantities. If a cart's speed changes or a cup has a temperature gradient, revisit the assumptions that treated speed or temperature as uniform. A convenient boundary and a short state description are useful choices only when they serve the investigation.

One cooling event, two system choices

1. Water alone
Include the water. The cup and room air are in the surroundings.
2. Across the water boundary
The stipulated transfer from warmer water to the cooler cup crosses this boundary.
3. Water plus cup
Include both participants. Their transfer is internal to this larger system.
4. Check the surroundings
Separately identify energy or matter exchanges with the outside air. State which are included or neglected.

The same water-to-cup energy transfer is classified differently when the chosen boundary changes. Neither choice by itself proves isolation.

Worked examples

The same position can belong to different states

In two stipulated trials, a cart's front mark is at 1.00 m at time zero. It moves at constant velocity +0.20 m/s in trial A and -0.20 m/s in trial B. Use the same fixed track origin, with positive to the right. Where is the mark after 2.0 s?

The position is initially the same, but the velocities differ. Positive and negative specify opposite directions.
For the stipulated constant velocities, displacement is velocity multiplied by elapsed time: A moves +0.40 m and B moves -0.40 m.
Add each displacement to 1.00 m: A reaches 1.40 m; B reaches 0.60 m.

A is at 1.40 m and B at 0.60 m. Position alone did not specify the motion needed by this model. The calculation assumes constant velocity; it does not establish that a real cart will maintain it.

Change the boundary and follow the same transfer

Consider one stipulated event: energy passes from warmer water to a cooler cup. Compare the system water alone with the system water plus cup. Does this event cross each system's boundary?

For water alone, the receiving cup is outside, so the transfer crosses the system boundary.
For water plus cup, both participants are inside, so the same transfer is internal.
Keep the physical event unchanged. Separately check any transfer to outside air.

It crosses the water-only boundary and is internal to water plus cup. The larger choice does not stop cooling or establish that the combined system is isolated.

A fixed region can contain changing matter

Choose a fixed region around a tank interior and its inlet and outlet cuts while water flows through. Then consider a sealed bottle heated by a warmer room while no matter crosses its boundary, and an ideal model with no matter or energy exchange. Classify each in the thermodynamic sense.

Water crosses the tank region's inlet and outlet cuts, so this is an open system. The matter occupying the region can change.
The sealed bottle exchanges no matter by assumption. The stipulated heating transfers energy from the room into it, so it is closed.
The ideal model excludes both exchanges, so it is isolated.

Open, closed and isolated, respectively. The tank's boundary is fixed even while water crosses it. Equal inflow and outflow would not remove those crossings or turn it into a closed system.

Try it yourself

You choose a sealed bottle and everything inside it as the system. Where is its outer boundary, and are the room air and tabletop part of the system?
Show the answer and reasoning
The boundary follows the bottle's outer surface. The room air and tabletop are in the surroundings.
This follows the stated choice of included objects. Contact with the table or air can still influence the bottle; being outside does not mean irrelevant.
A sealed rigid vessel receives energy through heating while no matter enters or leaves. Is it closed or isolated? Must its state stay unchanged?
Show the answer and reasoning
It is closed, not isolated. Its state can change.
The stated energy transfer rules out isolation. Closed excludes matter exchange but allows energy exchange; rigidity alone does not exclude heating.
A report says a cart is at 1.00 m and the water is liquid. Is that enough to predict the cart's next position or compare water cooling at different locations?
Show the answer and reasoning
No. The motion model needs velocity and its reference; the cooling description needs relevant temperature information, times and conditions.
A position omits how the cart is moving. A phase label omits temperature and spatial variation. Additional variables and a model of change are needed for the chosen questions.
An ideal sealed, insulated vessel receives energy from an external motor through a shaft turning a stirrer. No matter crosses, and no heat is transferred. Is the vessel isolated?
Show the answer and reasoning
No. It is closed and adiabatic in this model, but work transfers energy across its boundary.
Isolation excludes every energy transfer, not only heat. The external motor's mechanical action is an energy transfer even under the stipulated no-heat condition.

What to carry forward

Choose the system to fit the question and say what it includes.
A boundary distinguishes inside from outside; drawing it does not prevent an interaction.
A state description needs the variables and resolution required by its model.
An interaction can be internal or cross a boundary depending on the system choice.
In thermodynamics, closed excludes matter exchange; isolated excludes both matter and energy exchange.

References

Sources for the concepts and teaching approaches in this article.

Massachusetts Institute of Technology2 sources
1. Lectures on Thermodynamics, Chapter 1: Energy Accounting, Variables and Properties of SystemsGerbrand Ceder · Massachusetts Institute of TechnologyCourse notes · PDFocw.mit.eduRead source
2. MIT Unified Engineering Thermodynamics — State, heat and workIan A. Waitz (course instructor) · Massachusetts Institute of TechnologyCourse notesUnified Engineering Thermodynamics, Chapter 2: Thermodynamics Concepts Unified Engineering Thermodynamics, Chapter 3: Changing the State of a System with Heat and Workocw.mit.edu
NPTEL Advanced Engineering Thermodynamics — Systems and exchange classificationP. Mahanta · Indian Institute of Technology Guwahati / NPTELCourse notesAdvanced Engineering Thermodynamics, Module 1: Classical Thermodynamics, Lecture 1: Review of Thermodynamics — Concepts of classical thermodynamics Advanced Engineering Thermodynamics, Module 1: Classical Thermodynamics, Lecture 1: Review of Thermodynamics — System approach and classification of systemarchive.nptel.ac.in
University Physics Volume 1, 3.1 Position, Displacement, and Average VelocityWilliam Moebs, Samuel J. Ling, Jeff Sanny · OpenStax / Rice UniversityTextbook chapteropenstax.orgRead source
Introduction to Engineering Thermodynamics — Systems, state and boundary heatClaire Yu Yan · University of British Columbia Okanagan / BCcampusTextbook chapterIntroduction to Engineering Thermodynamics, 1.2 System and surroundings Introduction to Engineering Thermodynamics, 1.4 State, process, and cycle Introduction to Engineering Thermodynamics, 4.2 Heat transfer across a boundarypressbooks.bccampus.ca