Thermodynamic Terms and Systems

System, surroundings, boundary. In any thermodynamic problem, the universe is split in two: the system is the specific part being studied — a reaction flask, a gas trapped in a cylinder, a beaker of solution — and the surroundings is everything else that could interact with it. The boundary separates the two; it can be a real, physical wall (glass, metal) or an imaginary surface drawn just to mark where the system ends. Nothing in a thermodynamic argument makes sense until this division is fixed first.

Three types of system. Systems are classified purely by what the boundary permits to cross it — matter, energy, or neither:

• Open system: both matter and energy cross the boundary freely. Hot tea in an open cup loses both vapour (matter) and heat (energy) to the room.
• Closed system: only energy crosses, matter does not. A sealed gas cylinder that can still be heated or cooled is closed — no gas escapes, but heat and work can be exchanged.
• Isolated system: neither matter nor energy crosses. An ideal, perfectly insulated thermos flask approximates this; nothing enters or leaves in either form.

State functions versus path functions. The state of a system is fixed once its macroscopic properties — pressure $P$, volume $V$, temperature $T$, amount $n$ — are known. A property that depends only on this state, and not on the route by which the system arrived there, is a state function; internal energy $U$, enthalpy $H$, entropy $S$, and Gibbs energy $G$ are all state functions. A property that depends on the actual path taken is a path function; heat $q$ and work $w$ are the two path functions you will meet throughout this chapter. The distinction matters because a state function's change between two fixed states is always the same number, however messy or roundabout the process — a state function behaves like the difference in altitude between a base camp and a summit, which does not care whether you took the direct ridge or the long scenic route, while the distance walked (a path function) very much does.

Extensive versus intensive properties. Properties also split by how they respond to the amount of substance present:

• Extensive properties scale with the quantity of matter — mass, volume, internal energy, and enthalpy all double if you double the sample. They are additive: the volume of two identical flasks together is the sum of each.
• Intensive properties do not depend on how much matter is present — temperature, pressure, density, and molar volume stay the same whether you have one gram or one kilogram of a uniform sample.

Process conditions. Several standard conditions recur throughout the chapter, each defined by holding one variable fixed:

where: $\Delta T$, $\Delta P$, $\Delta V$ are the changes in temperature, pressure, and volume of the system over the process, and $q$ is the heat exchanged with the surroundings. A process can satisfy more than one of these at once (a reversible isothermal expansion of an ideal gas is both isothermal and, separately, has $\Delta U = 0$), but each label refers strictly to the one variable named.

This topic is descriptive rather than a calculation, but the classifications above are not arbitrary labels — each one follows from a physical argument about what the boundary of the system actually permits.

Why the three system types are exhaustive. A boundary can only do one of three things that matter here: let both matter and energy cross, let only energy cross, or let neither cross. (Letting only matter cross without any energy almost never happens physically, since transferring matter across a real boundary nearly always drags some heat with it.) Real containers are rarely perfect — a "closed" flask still loses a trace of heat over long times, and an "isolated" thermos is only isolated for the timescale of the experiment — so the classification describes the dominant behaviour of the boundary under the conditions of the problem, not an absolute guarantee.

Why state functions are path-independent. A state function is, by definition, a property of the system's current condition alone — a mathematical function of $P$, $T$, $V$, $n$ evaluated at that instant, the way altitude is a function of position on a map. Two paths that start and end at the same $(P, T, V, n)$ give identical values of $U$, $H$, $S$, or $G$ at the end, because the function only looks at where you are, never how you got there. Heat $q$ and work $w$ carry no such guarantee: they are processes, quantities of energy transferred while moving between states, and different routes (reversible versus irreversible, constant pressure versus constant volume) genuinely transfer different amounts of each between the same two endpoints. What is guaranteed instead — the seed of the first law, met properly later in this unit — is that the combination $q + w$ always equals the same $\Delta U$ regardless of path, even though $q$ and $w$ separately do not.

Why extensive properties are additive but intensive ones are not. An extensive property is built by summing a microscopic quantity (mass, energy, volume) over every parcel of the system, so two identical systems placed side by side simply add their extensive properties. An intensive property is typically a ratio of two extensive properties — density is mass divided by volume, molar volume is volume divided by moles — and a ratio of two proportional quantities cancels the "amount," leaving a number that describes the substance itself. That is why intensive properties, not extensive ones, identify a substance: the density of water is $1\ \text{g/mL}$ whether you have a drop or a swimming pool.

Problem: Classify each situation as an open, closed, or isolated system, and separately state whether the underlined quantity is a state function or a path function and whether it is extensive or intensive: (a) an open beaker of boiling water, considering the water as the system; (b) a sealed, rigid, perfectly insulated steel cylinder of gas; (c) for the gas in (b), its volume; (d) the heat released when the gas in (b) is allowed to do work against a piston in a separate, non-insulated experiment.

Step 1. Classify the beaker of boiling water. Steam (matter) escapes continuously into the air, and heat also flows across the beaker's open boundary to the surroundings. Since both matter and energy cross, this is an open system.

Step 2. Classify the sealed, rigid, insulated cylinder. It is sealed, so no gas can escape (no matter crosses). It is rigid, so no expansion work is possible, and it is perfectly insulated, so no heat crosses either. With neither matter nor energy crossing, this is an isolated system.

Step 3. Classify the volume of the gas in (b). Volume depends only on the current amount, pressure, and temperature of the gas — not on the sequence of steps used to reach that state — so it is a state function. It scales directly with how much gas is present, so it is also extensive.

Step 4. Classify the heat in the separate, non-insulated experiment. Once the cylinder is no longer insulated and can do work against a piston, the heat released depends on exactly how the expansion is carried out (quickly against a fixed external pressure, or slowly and reversibly) — for the same start and end states, different routes give different values of $q$. So heat here is a path function; it is conventionally treated as extensive because it scales with the amount of substance undergoing the process.

Answer: (a) open system; (b) isolated system; (c) volume is a state function and extensive; (d) heat is a path function and (conventionally) extensive.

• Treating "closed" as if it meant "isolated" — a closed system can still absorb or release heat and do work; only matter is blocked from crossing.
• Speaking of a system as "possessing" heat or work the way it possesses internal energy. It does not: internal energy is a definite property of a state, while heat and work only exist as quantities transferred during a process.
• Assuming $q$ and $w$ must each be the same for two processes with the same start and end states, when only their sum, $\Delta U$, is path-independent — $q$ and $w$ individually can and usually do differ across different routes.
• Mixing up extensive and intensive properties, especially forgetting that a ratio of two extensive quantities (density = mass/volume, molar volume = volume/moles) is intensive even though both quantities used to build it are extensive.

Ask the tutor: Want to work through a few more tricky classify-the-system scenarios, or see how state functions connect directly into the first law of thermodynamics next?