Systems, Surroundings, and Boundaries

Boil water in a sealed thermos and nothing gets in or out but heat can still slip through the walls. Boil it in an open kettle and steam escapes freely into the kitchen air. These two setups look similar but obey completely different bookkeeping rules in thermodynamics. Before you can track energy or matter through any chemical process, you must draw a line and name what is inside it and what is outside it. That line is the boundary, the inside is the system, and everything else is the surroundings. This sounds trivial, but almost every error in a beginning thermodynamics problem traces back to an unclear or inconsistent boundary. Get the system definition wrong, and every heat, work, and energy calculation that follows is wrong too. This article defines the three system types: open, closed, and isolated. It explains what a boundary actually controls. It introduces the extensive versus intensive property distinction, which determines how properties scale with system size. These ideas are the scaffolding for everything that follows: state functions, internal energy, heat, and work.

Key takeaways

A thermodynamic system is the part of the universe you choose to study; the surroundings are everything else; the boundary is the real or imaginary surface separating them.
Open systems exchange both matter and energy with the surroundings; closed systems exchange energy only; isolated systems exchange neither.
Boundaries are classified by what they permit: permeable or impermeable (matter), diathermic or adiabatic (heat), rigid or movable (work).
Extensive properties (mass, volume, internal energy) scale with the amount of substance; intensive properties (temperature, pressure, density, molar quantities) do not.
The ratio of two extensive properties is always intensive — this is how molar and specific quantities are built.
Key idea: every thermodynamic quantity you will ever compute depends on first fixing, and never silently changing, the boundary that defines the system.

The core insight

A thermodynamic system is not a physical object but a deliberate choice, a labeled region of space whose boundary specifies exactly which exchanges with the rest of the universe — matter, heat, work — are permitted or forbidden, and that single choice determines every energy balance you can legitimately write down for it.

The physical picture

Imagine a chemist studying a reaction happening inside a flask. The system is whatever the chemist has decided to study: perhaps the reacting chemicals, perhaps the chemicals plus the solvent, perhaps the flask's contents together with the flask itself. The surroundings are literally everything else in the universe capable of interacting with the system — the air in the room, the lab bench, the thermostatted water bath, ultimately the rest of the cosmos, though in practice only nearby matter matters. The boundary is the dividing surface, real (glass walls) or imagined (a mathematical surface drawn in open air), across which matter and energy may or may not pass. Three canonical system types cover essentially every case you will meet: An open system exchanges both matter and energy with its surroundings. A beaker of water evaporating on an open bench, a living cell, or an open flame are open systems: mass leaves or enters, and heat crosses the boundary too. A closed system exchanges energy (as heat and/or work) but not matter. A sealed, rigid metal can heated on a stove is closed: no substance escapes, but heat certainly flows in, and if the can can expand, work is done too. Most introductory thermodynamics — and essentially all of classical thermochemistry — is built on closed systems, because they are the simplest case where you must still account for energy flow. An isolated system exchanges neither matter nor energy with anything outside. A perfect (idealized) thermos flask with rigid, non-conducting walls approximates this. No real system is perfectly isolated, but the universe as a whole is defined, by convention, to be an isolated system: energy is neither created nor destroyed within it, which is exactly the content of the First Law. The boundary itself is characterized by what it lets through. A boundary is permeable if matter can cross it and impermeable if not. It is diathermic if heat can cross it (allowing thermal equilibration with the surroundings) and adiabatic if no heat can cross it, regardless of any temperature difference. It is rigid if its volume is fixed and movable (or flexible) if it can expand or contract, which is the condition required for pressure–volume work to occur. These three independent yes/no choices — permeable, diathermic, movable — fully specify a system's possible interactions with the world, and every system type above is just a particular combination of them. A second, equally important distinction concerns properties rather than boundaries: how a measured quantity behaves when you scale the system up or down. An extensive property depends on the size (the amount of substance) of the system: mass $m$ , volume $V$ , total internal energy $U$ , total entropy $S$ , and total heat capacity $C$ are all extensive — double the amount of substance at fixed composition and each one doubles. An intensive property does not depend on the amount of substance: temperature $T$ , pressure $p$ , density $\rho$ , mole fraction, and any molar or specific quantity (molar volume $V_m$ , molar heat capacity $C_m$ , specific heat capacity $c$ ) are intensive. Crucially, the ratio of two extensive properties is always intensive, which is precisely how molar quantities are constructed from total ones.

Figure

Figure 1. Three system types classified by what crosses the boundary

Figure

Figure 2. Extensive vs intensive: splitting a system in half

The core relations

X_{\text{extensive}}(n) = n \cdot X_m

where: $X$ is any extensive property (e.g. $V$ , $U$ ), $n$ is the amount of substance, and $X_m$ is the corresponding molar (intensive) quantity.

X_m = \frac{X}{n}

where: dividing one extensive property by another (here, amount of substance) always produces an intensive quantity.

\rho = \frac{m}{V}

where: $\rho$ is density (intensive), $m$ is mass and $V$ is volume (both extensive) — the classic example of an intensive ratio.

\Delta U_{\text{universe}} = \Delta U_{\text{system}} + \Delta U_{\text{surroundings}} = 0

where: this holds because the system-plus-surroundings together form an isolated system, the statement underlying the First Law.

Derivation AWhy a ratio of extensive properties must be intensive

Goal. Show rigorously that if $X$ and $Y$ are both extensive properties of a homogeneous system, their ratio $X/Y$ is necessarily intensive.

Step 1. Define extensivity precisely. A property $X$ is extensive if, when the amount of substance is scaled by a factor $\lambda > 0$ at fixed intensive conditions (same $T$ , $p$ , composition), the property scales by the same factor:

X(\lambda n) = \lambda \, X(n).

This is the mathematical statement that $X$ is a homogeneous function of degree 1 in the size variable $n$ .

Step 2. Apply the same scaling to a second extensive property $Y$ . By the identical definition,

Y(\lambda n) = \lambda \, Y(n).

Step 3. Form the ratio at the scaled size. Divide the two scaled expressions:

\frac{X(\lambda n)}{Y(\lambda n)} = \frac{\lambda X(n)}{\lambda Y(n)} = \frac{X(n)}{Y(n)}.

Step 4. Interpret the result. The scaling factor $\lambda$ cancels exactly, so the ratio $X/Y$ takes the same value regardless of how large or small a sample you examine, provided $T$ , $p$ , and composition are held fixed. A property whose value is unchanged under a change of system size is, by definition, intensive.

Step 5. Concrete check. Take $X = V$ (volume) and $Y = n$ (amount of substance). Both are extensive: doubling the sample at fixed $T,p$ doubles both $V$ and $n$ . Their ratio $V/n = V_m$ , the molar volume, is therefore intensive — consistent with the fact that molar volume depends only on $T$ and $p$ for a given substance, never on how much of it you have.

\boxed{\dfrac{X}{Y} \text{ is intensive whenever } X \text{ and } Y \text{ are both extensive.}}

Worked examples

Example 1 — Classifying a real setup (foundational). A chemist places 25.0 mL of aqueous NaCl solution in an open, uncapped beaker on a laboratory bench and monitors it as water evaporates and the solution cools slightly by exchanging heat with the room. Step 1 — define the system. Take the system to be the solution inside the beaker (the dissolved NaCl plus the liquid water). Step 2 — check for matter exchange. Water vapor visibly leaves the open beaker into the room air, and the beaker is open to the atmosphere, so matter crosses the boundary. Matter exchange is possible: the boundary is permeable. Step 3 — check for energy exchange. The glass beaker wall is thin and thermally conducting, and the top is fully open, so heat flows between the solution and the room until thermal equilibrium is approached. The boundary is diathermic. Step 4 — check for work. Because the beaker is open to the atmosphere, the "gas phase" above the solution is not confined; there is no well-defined piston, but the system's volume is technically free to change as liquid is lost, so mechanical work exchange with the atmosphere is not excluded either. Step 5 — classify. Since both matter and energy freely cross the boundary, this is an open system. If the chemist instead sealed the beaker with a tight cap (no vapor escapes, but the glass still conducts heat), the same contents would become a closed system. If further wrapped in a perfect vacuum-insulated, rigid jacket, it would approximate an isolated system. Sanity check. This matches everyday intuition: an uncovered cup of coffee loses both steam (matter) and heat (energy) to the room — obviously open — while a thermos of the same coffee loses almost neither, over the timescale of interest — closer to isolated.

Example 2 — Extensive vs. intensive quantities in a calorimetry setup (applied, exam-level). A bomb calorimeter contains 1.250 g of benzoic acid (molar mass $M = 122.12\ \text{g mol}^{-1}$ ) burned completely in excess oxygen inside a rigid, sealed steel bomb immersed in 1.200 kg of water. The calorimeter's total heat capacity is $C_{\text{cal}} = 10.15\ \text{kJ K}^{-1}$ , and the measured temperature rise is $\Delta T = 3.052\ \text{K}$ . Step 1 — identify the system and boundary. The system is chosen as the bomb's rigid interior (benzoic acid, oxygen, and combustion products). The bomb wall is rigid (no $p$ – $V$ work possible) and impermeable (sealed, no matter crosses it), but it does allow heat to flow into the surrounding water bath, so on the timescale of interest the working boundary between "bomb + water + calorimeter hardware" and "the rest of the lab" is effectively adiabatic (well-insulated calorimeter), while the inner boundary between the bomb and the water bath is diathermic. This layered-boundary description is exactly why the calorimeter as a whole is treated as an isolated system. Step 2 — total heat released (an extensive quantity). Treating the entire calorimeter assembly as isolated, the heat released by the reaction is absorbed entirely by the calorimeter (water + hardware):

q_{\text{released}} = C_{\text{cal}} \times \Delta T = 10.15\ \text{kJ K}^{-1} \times 3.052\ \text{K} = 30.98\ \text{kJ}.

This is an extensive quantity: it depends on how much benzoic acid (1.250 g, specifically) was actually burned. Step 3 — convert to moles burned.

n = \frac{1.250\ \text{g}}{122.12\ \text{g mol}^{-1}} = 0.010236\ \text{mol}.

Step 4 — compute the molar internal energy of combustion (an intensive quantity). Divide the extensive heat by the extensive amount:

\Delta_c U_m = -\frac{30.98\ \text{kJ}}{0.010236\ \text{mol}} = -3026\ \text{kJ mol}^{-1}.

The negative sign is assigned because the reaction released heat to the calorimeter; internal energy of the system (reacting mixture) decreased. This value is intensive: it does not depend on whether you had burned 1.250 g or 12.50 g — burning ten times as much benzoic acid would release ten times the heat (30.98 kJ → 309.8 kJ), because $q$ is extensive, but $\Delta_c U_m$ would still come out to the same $-3026$ kJ mol⁻¹. Step 5 — sanity check against the literature. The accepted standard molar internal energy of combustion of benzoic acid is $-3226$ kJ mol⁻¹ (a value so reproducible it is the standard calibration reactant for bomb calorimetry). Our worked number, $-3026\ \text{kJ mol}^{-1}$ , is of the correct order of magnitude and sign; the roughly 6% discrepancy is consistent with using illustrative rather than exactly calibrated input numbers, and the exercise's purpose — distinguishing the extensive heat $q$ from the intensive molar quantity $\Delta_c U_m$ — is unaffected by the precise calibration constant used.

Limiting cases & common traps

Situation	Correct classification	Common error
Reaction in a sealed, rigid ampoule	Closed system (energy only, no work possible: rigid)	Assuming "sealed" automatically means isolated
Human body	Open system (eats, breathes, radiates heat)	Treating living organisms as closed systems
Entire universe	Isolated system, by definition	Trying to apply this label to any lab-scale apparatus
Ideal gas expanding against a piston	Closed system if piston prevents matter loss; boundary is movable, diathermic or adiabatic depending on cylinder wall	Confusing "movable boundary" with "open system"
Molar heat capacity $C_m$	Intensive	Assuming $C_m$ scales with sample size like $C$ does

The chemist behind it

The system/surroundings/boundary framework was formalized during the classical development of thermodynamics in the mid-to-late 19th century, but its rigorous articulation for chemistry owes an enormous debt to the German physicist Rudolf Clausius, who sharpened the concept of "the system" while developing the mathematical statement of the First and Second Laws. Clausius insisted on treating the "working substance" and its surroundings as cleanly separable for the purposes of energy accounting — precisely the move that lets a chemist isolate a beaker of reacting solution and write a clean energy balance for it alone, trusting that whatever the surroundings do is bookkept separately.

Origins · 1 minRudolf Clausius and how this was discovered

Rudolf Clausius

1822–1888 · German physicist who coined "entropy" and gave the First and Second Laws their modern mathematical form, making system/surroundings bookkeeping rigorous

Ask the tutor: How does the choice of system and boundary change the signs and values of $q$ and $w$ when I apply the First Law to a real reaction?

Is the human body an open, closed, or isolated system

The human body is an open system. It continuously exchanges matter with its surroundings, through breathing, eating, drinking, sweating, and excretion, and it exchanges energy as heat and as work performed on or by the environment. This is why living organisms require a constant net inflow of matter and energy to maintain their internal organization; a closed or isolated system could not sustain the ongoing biochemical turnover that keeps an organism alive.

Can a boundary be permeable to some substances but not others

Yes, and this is common in chemistry. A semipermeable membrane, such as the one used in osmosis experiments, allows small solvent molecules like water to cross while blocking larger solute molecules or ions. Such a system is neither fully open nor fully closed in the simple sense; it is often described as a special case of an open system with selective permeability, and it is central to topics like osmotic pressure and dialysis.

Why does the extensive/intensive distinction matter for thermochemistry

Thermochemical data are almost always reported as intensive, molar quantities, such as $\Delta_c H_m$ in kJ per mole, precisely so that they are transferable between experiments run with different sample sizes. If you report only the raw extensive heat released, $q$ , that number is meaningless without also stating exactly how much material reacted. Converting an extensive measurement into an intensive molar quantity, by dividing by moles, is what makes tabulated thermodynamic data universally reusable.

Does choosing the system boundary differently change the physics of what actually happens

No — the physical process is unaffected by how you draw the boundary, but your energy accounting changes completely depending on where you draw it. If you define the system as just the reacting chemicals, the solvent is part of the surroundings and its heating counts as heat transferred out of the system. If you redefine the system to include the solvent too, that same energy transfer becomes an internal redistribution, not a boundary crossing. Consistency, not correctness of one choice over another, is what matters.

How does this connect to state functions and the First Law, covered next

Once a system, its boundary, and its type are fixed, you can ask how its internal energy $U$ changes due to heat $q$ and work $w$ crossing that specific boundary. That relationship, $\Delta U = q + w$ , is the First Law, and it depends entirely on having unambiguously defined the boundary first. The next articles build directly on this: state functions describe properties of the system itself, while heat and work describe processes across the boundary you have just learned to define.