Fundamentals (Thermodynamics)

Thermal equilibrium concepts, zeroth law, empirical temperature, and thermometric scales.

Classical thermodynamics is the branch of physics dedicated to studying energy transformations, heat transfer, and mechanical work in macroscopic systems. Unlike Newtonian mechanics, which tracks individual trajectories of point particles, thermodynamics describes the overall state of matter through macroscopic observables accessible to measurement, formulating universal principles that remain valid regardless of the specific microscopic atomic models of the substance.

Systems, Boundaries, and Surroundings

The initial foundation of any thermodynamic analysis requires isolating a specific region in space:

• Thermodynamic System: The designated quantity of matter or radiation selected for investigation.
• Boundary or Wall: The real or conceptual surface separating the system from the rest of the universe. Boundaries can be adiabatic (preventing any thermal energy transfer), diathermic (allowing heat exchange), rigid (prohibiting mechanical boundary deformation work), or permeable (permitting mass transfer).
• Surroundings or Environment: Everything external to the boundary capable of interacting energetically with the system.

Depending on boundary properties, systems are classified as open (exchanging both matter and energy), closed (exchanging energy but not matter), and isolated (exchanging neither matter nor energy with surroundings).

State Variables and Thermodynamic Equilibrium

A system is in a state of thermodynamic equilibrium when no macroscopic spontaneous changes occur over time. This state demands the simultaneous fulfillment of three distinct criteria:

1. Mechanical Equilibrium: Zero net internal and boundary forces, yielding a spatially uniform pressure distribution.
2. Thermal Equilibrium: Spatially uniform temperature throughout the system matching that of the environment.
3. Chemical Equilibrium: Homogeneous chemical potentials without net reaction rates or diffusive mass fluxes.

Thermodynamic states are quantitatively described by state variables, categorized into:

• Intensive Variables: Local properties independent of total system size or mass, such as temperature $T$, pressure $P$, and mass density $\rho$.
• Extensive Variables: Global quantities directly proportional to the total amount of substance, such as volume $V$, internal energy $U$, and entropy $S$.

The Zeroth Law and the Concept of Temperature

The Zeroth Law of Thermodynamics asserts that if two systems $A$ and $B$ are individually in thermal equilibrium with a third system $C$, they are necessarily in thermal equilibrium with each other. This transitive relationship justifies defining temperature as an intrinsic scalar property that governs whether two bodies placed in thermal contact will exchange heat, establishing the operational foundation for thermometry and temperature scale standardization.