System, surroundings and boundary
Thermodynamics is a macroscopic science. It deals with bulk matter and ignores the molecular constitution entirely; the state of a gas is described by a handful of measurable quantities such as pressure, volume, temperature, mass and composition. Before we can talk about temperature we must agree on what we are studying and what we are not.
A thermodynamic system is a definite quantity of matter set apart for study — the gas in a cylinder, the water in a beaker. Everything outside it that can influence it is the surroundings. The surface that separates the two, real or imaginary, is the boundary (also called the wall). The nature of that boundary controls what can cross it, and therefore whether the system reaches equilibrium with its surroundings at all.
Open, closed and isolated systems
Systems are classified by what their boundary lets pass. The distinction matters because an isolated system left to itself settles into a single unchanging equilibrium state, while open and closed systems keep exchanging with the surroundings until equilibrium is reached.
| System type | Exchanges mass? | Exchanges energy? | Example |
|---|---|---|---|
| Open | Yes | Yes | A water heater — water and heat both cross the boundary |
| Closed | No | Yes | Gas in a cylinder fitted with a piston — energy crosses, mass does not |
| Isolated | No | No | An ideal filled thermos flask — neither mass nor energy crosses |
A gas inside a closed rigid container, completely insulated from its surroundings, with fixed pressure, volume, temperature, mass and composition that do not change in time, is the textbook picture of a system in thermodynamic equilibrium. Note the contrast with mechanics: there, equilibrium means net force and torque are zero. In thermodynamics, equilibrium means the macroscopic variables that characterise the system do not change with time.
Thermal equilibrium
Full thermodynamic equilibrium actually bundles three separate conditions — mechanical equilibrium (no unbalanced forces or stresses within the system), chemical equilibrium (all possible reactions have ceased), and thermal equilibrium. For the Zeroth law it is the thermal part that matters.
Two systems are in thermal equilibrium when, placed in thermal contact, there is no net flow of heat between them and their macroscopic variables stop changing. Whether equilibrium is reached at all depends on the surroundings and, crucially, on the nature of the wall separating the systems.
Consider two gases A and B in separate containers, with states $(P_A, V_A)$ and $(P_B, V_B)$. If the wall between them blocks heat, any pair of values for A stays in equilibrium with any pair for B — nothing changes, because nothing can cross. If instead the wall conducts heat, the macroscopic variables of A and B change spontaneously until both reach equilibrium states $(P_A', V_A')$ and $(P_B', V_B')$, after which there is no further energy flow. We then say A is in thermal equilibrium with B. The variable that turns out to be equal for the two systems at this point is their temperature.
Adiabatic vs diathermic walls
The two kinds of wall that control heat flow have precise names, and NEET tests the distinction directly.
| Property | Adiabatic wall | Diathermic wall |
|---|---|---|
| Nature | Insulating | Conducting |
| Allows heat flow? | No — blocks energy (heat) | Yes — allows energy (heat) to flow |
| Effect on two systems | Each keeps its own state; any pair of states stays "in equilibrium" trivially | States change spontaneously until a common thermal equilibrium is reached |
| Reaches thermal equilibrium? | Not through the wall | Yes, in due course |
| Idealised example | Thick foam, vacuum flask wall | Thin metal sheet |
An adiabatic wall isolates: it does not allow the flow of heat. A diathermic wall connects: it permits heat to pass, so two systems separated by it equalise their temperatures and settle into equilibrium. These walls are idealisations — perfect insulators and perfect conductors do not exist — but they let us reason cleanly about which systems can exchange heat with which.
The Zeroth law statement
Now place three systems in the arrangement that gives the law its content. Systems A and B are separated from each other by an adiabatic wall, but each is in contact with a third system C through a diathermic wall. Left alone, A and B each come to thermal equilibrium with C. Next, swap the walls: put a conducting wall between A and B, and insulate C from both with an adiabatic wall. Experiment shows that the states of A and B do not change any further — they are already in thermal equilibrium with each other.
Zeroth law of thermodynamics. Two systems in thermal equilibrium with a third system separately are in thermal equilibrium with each other.
The history explains the odd name. R. H. Fowler formulated this law in 1931 — long after the first and second laws of thermodynamics had already been stated and numbered in the nineteenth century. Because the law is logically prior to those (it underpins the very idea of temperature they use), it was given the number zero rather than tacked on as a third or fourth law.
How the law defines temperature
The Zeroth law is not a triviality. It asserts something experiment confirms but logic alone cannot guarantee: that "being in thermal equilibrium with" behaves like equality. From it follows the existence of a single physical quantity, shared by all systems mutually in thermal equilibrium. That quantity is named temperature, $T$.
Written out, if A and B are each separately in equilibrium with C, then
$$T_A = T_C \quad \text{and} \quad T_B = T_C \;\;\Rightarrow\;\; T_A = T_B,$$
so A and B are in thermal equilibrium. The chain is exactly the chain of the law. This gives the operational definition used throughout the rest of thermodynamics: temperature is the property of a body that determines whether or not it is in thermal equilibrium with other bodies. Two bodies are at the same temperature precisely when they would exchange no net heat on contact.
A thermometer is the "third system" C. It is brought to equilibrium with a body, reads its own state, and the Zeroth law guarantees any two bodies giving the same reading are at the same temperature. The next step — assigning numbers — is taken up in the first law and beyond.
Triple point as a fixed temperature
Having defined temperature, thermodynamics needs reproducible reference states to assign numbers to it. The most stable such state is the triple point — the single combination of temperature and pressure at which the solid, liquid and vapour phases of a pure substance coexist in equilibrium.
On a pressure–temperature phase diagram, the fusion curve (solid–liquid), the vaporisation curve (liquid–vapour) and the sublimation curve (solid–vapour) all meet at one point. That meeting point is the triple point, and it occurs at precisely fixed values of temperature and pressure — it cannot be shifted without leaving the three-phase coexistence. For water this makes the triple point an exceptionally reproducible standard, which is why the Kelvin scale of thermometry uses the triple point of water as a fixed reference point.
The Zeroth law in one breath
- A system is the matter under study; the surroundings lie outside; the boundary (wall) separates them. Open exchanges mass and energy, closed only energy, isolated neither.
- Thermal equilibrium = no net heat flow between bodies in contact; their macroscopic variables stop changing.
- Adiabatic wall = insulating, blocks heat. Diathermic wall = conducting, allows heat and lets systems equilibrate.
- Zeroth law: if A and B are each in thermal equilibrium with C, then A and B are in thermal equilibrium with each other.
- The law guarantees a common property at equilibrium — temperature. $T_A = T_C$ and $T_B = T_C \Rightarrow T_A = T_B$.
- Zeroth → temperature, First → internal energy, Second → entropy. Equilibrium needs equal temperature, not equal heat content.
- The triple point fixes a unique $(T, P)$ where solid, liquid and vapour coexist — water's triple point is a Kelvin-scale reference.