System, Boundary and Surroundings

System

The quantity of matter or region of space chosen for study. It is a choice, not a property of the apparatus.

Boundary

The surface separating system from surroundings. Real or imaginary, fixed or moving, and of zero thickness — so it contains no mass and stores no energy.

Surroundings

Everything outside the boundary. In practice, everything that matters is the immediate surroundings.

Universe

System plus surroundings — the one genuinely isolated system there is.

Adiabatic is not a fourth row. It says only that *heat* does not cross — work still may, and an adiabatic compression does a great deal of work. Treating adiabatic as a synonym for isolated is one of the most persistent errors in the subject.

Take a gas in a cylinder with a piston, heated from below. Three legitimate boundaries give three different — and all correct — analyses.

1. 1Boundary A: the gas only. A closed system with fixed mass. Heat crosses in, work crosses out as the piston is pushed. ΔU = Q − W, where U is the internal energy of the gas.
2. 2Boundary B: gas, cylinder and piston. Still closed, but the metal is now inside, so its internal energy is part of U. Crucially, piston friction is now internal — it no longer represents energy leaving, only energy moving about inside.
3. 3Boundary C: a fixed volume the gas flows through. An open system. Mass crosses, and mass carries energy with it, so the balance gains flow terms.

Nothing physical differs between the three. The apparatus is identical, the flame is identical, the piston moves identically. Only the accounting changes — which is exactly why leaving the choice implicit is so damaging.

Mass crossing a boundary carries energy with it: internal energy u, kinetic energy V²/2, potential energy gz, and the flow work pv needed to push it across against the pressure there.

Since u and pv always appear together for flowing matter, they are grouped as enthalpy h = u + pv. Enthalpy is not a new kind of energy; it is a bookkeeping convenience that exists precisely because of open systems.

This is why the steady flow energy equation is written in h rather than u, and why turbine, nozzle and compressor problems are all enthalpy problems.

• Q is positive when heat enters the system — because that is what you pay for in a heat engine.
• W is positive when work is done by the system — because that is what you are trying to sell.
• So ΔU = Q − W reads as: stored equals in minus out.

A compressor comes out with negative W. That is not an error but the convention correctly reporting that work was supplied rather than produced.

Chemistry uses the opposite sign for work and writes ΔU = Q + W. Neither convention is more correct; mixing them within one problem is fatal, and knowing that both exist prevents a great deal of confusion when reading across textbooks.

Property

Any measurable characteristic of a system in equilibrium — pressure, temperature, volume, internal energy. Depends only on the current state, never on how it was reached.

Intensive vs extensive

Intensive properties (p, T, density) are independent of mass; extensive ones (V, U, m) scale with it. Divide an extensive property by mass and you get a specific property, which is intensive.

State

The condition of a system, fixed by its properties. For a simple compressible substance, any two independent intensive properties fix the state.

Process and cycle

A change of state is a process; a series of processes returning to the starting state is a cycle. Round a cycle every property change is zero — which is why ∮dU = 0 and heat engine analysis is possible.

Path function

Heat and work are not properties. They depend on the route taken, not just the endpoints — which is why they are written δQ and δW, and why a system contains internal energy but never 'contains heat'.