Systems, Walls and State Variables

Drawing the Boundary First

Thermodynamics begins by choosing a system and calling everything else the surroundings. What crosses the boundary is decided by the kind of wall:

An isolated system has adiabatic, rigid, impermeable walls and exchanges nothing at all.

The state of a simple system is fixed by a small number of state variables, split by how they scale. Extensive variables double when you double the system: volume, internal energy, entropy, mass. Intensive ones do not: pressure, temperature, density. Every extensive variable has an intensive partner it pairs with in the energy balance, $P$ with $V$, $T$ with $S$, $\mu$ with $N$.

Dividing one extensive variable by another gives an intensive one, which is why molar and specific quantities are so useful: $v = V/n$ is intensive and describes the substance rather than the sample.

Thermodynamic equilibrium requires three conditions at once, thermal (uniform $T$), mechanical (uniform $P$), and chemical (uniform $\mu$). Only in equilibrium do the state variables have well-defined values at all, which is why non-equilibrium states cannot be plotted as points on a $P$-$V$ diagram.

A quasistatic process passes through a continuous sequence of equilibrium states, slowly enough that the system is never appreciably out of balance. Every quasistatic path can be drawn as a curve; a violent, irreversible one cannot, and is conventionally shown as a dashed line between endpoints only.

Common pitfall: calling any slow process reversible. Quasistatic is necessary but not sufficient, slow friction is still dissipative. Reversibility additionally requires that no entropy be generated, so that the system and its surroundings can both be restored.