Thermodynamics

Thermodynamics is the branch of physics concerned with energy, heat, work, and the macroscopic properties of matter. It describes how systems exchange energy, which transformations are possible, and the conditions for equilibrium. Its principles apply to engines, chemical reactions, materials, and many natural processes. Classical thermodynamics uses measurable bulk properties without requiring a detailed account of individual particles; statistical mechanics supplies a microscopic interpretation. (ocw.mit.edu)

Historical development

Thermodynamics developed partly from attempts to understand and improve the steam engine. In 1824, Sadi Carnot published an analysis of the limits of heat-engine performance. Although his reasoning used the subsequently abandoned caloric theory of heat, his treatment of ideal reversible engines helped establish the foundations of the subject. (aps.org)

During the nineteenth century, experiments by James Prescott Joule established quantitative relationships between mechanical work and heat. Rudolf Clausius and William Thomson, later Lord Kelvin, helped formulate the principles now identified as the first and second laws. These developments replaced the idea of heat as a conserved substance with an account of energy conservation and constraints on energy conversion. (aps.org)

Systems, states, and processes

A thermodynamic system is a selected quantity of matter or region of space separated conceptually from its surroundings. An open system can exchange matter and energy; a closed system exchanges energy but not matter; an isolated system exchanges neither. The boundary may be fixed or moving, physical or imaginary. Choosing it determines which transfers enter the analysis. (ocw.mit.edu)

A state is specified by properties such as temperature, pressure, volume, composition, and internal energy. Intensive properties, including temperature and pressure, do not scale with system size; extensive properties, including volume and energy, generally do. In thermodynamic equilibrium, no unbalanced thermal, mechanical, or chemical driving forces produce macroscopic change under the imposed constraints. (ocw.mit.edu)

An equation of state relates state variables. For an ideal gas,

where $p$ is pressure, $V$ volume, $n$ amount of substance, $R$ the gas constant, and $T$ absolute temperature. A process connects states: isothermal processes maintain constant temperature, whereas adiabatic processes involve no heat transfer. A reversible process is an ideal limit in which system and surroundings can both be restored without a net change elsewhere. (ocw.mit.edu)

The laws of thermodynamics

The zeroth law states that two systems each in thermal equilibrium with a third are in thermal equilibrium with one another. It supports the definition of temperature and the use of thermometers. (ocw.mit.edu)

The first law expresses energy conservation. For a closed system with negligible changes in bulk kinetic and potential energy,

where $Q$ is heat supplied to the system and $W$ is work done by it. Other sign conventions are used, particularly when work done on the system is defined as positive. Heat and work are transfers across a boundary, not substances stored within a system. Unlike internal energy, their values depend on the process path. (openstax.org)

The second law introduces entropy, a state function constraining the direction of change. The entropy of an isolated system cannot decrease: it remains constant in reversible processes and increases in irreversible ones. A nonisolated system can lose entropy by transferring it to its surroundings. For a reversible heat transfer,

Equivalent formulations prohibit a cyclic engine whose sole effect is converting heat from a single reservoir entirely into work, and prohibit transferring heat from colder to hotter bodies without another compensating effect. (openstax.org)

The third law, in its perfect-crystal formulation, states that the entropy of a pure, perfectly ordered crystal is zero at absolute zero. It provides a reference for calculating absolute entropies; substances retaining configurational disorder may exhibit residual entropy. (openstax.org)

Potentials and equilibrium

Thermodynamic potentials combine state variables into functions suited to different experimental constraints. Enthalpy is $H=U+pV$; Helmholtz free energy is $F=U-TS$; and Gibbs free energy is $G=H-TS$. These functions allow equilibrium criteria to be expressed in terms of system properties rather than explicitly tracking the surroundings. (ocw.mit.edu)

For a closed system at fixed temperature and pressure, with no imposed non-expansion work, spontaneous change lowers Gibbs free energy, and stable equilibrium corresponds to its minimum under the applicable constraints. This criterion is central to chemistry, where it determines the favorable direction of a chemical reaction and helps describe phase transitions. Thermodynamic favorability does not determine reaction speed: a favorable transformation may proceed extremely slowly because of kinetic barriers. (live.ocw.mit.edu)

Microscopic interpretation and applications

Statistical mechanics connects bulk properties with the behavior of atoms and molecules. For equally probable accessible microstates, Boltzmann’s relation,

relates entropy to their number $\Omega$. This interpretation makes entropy more precise than the informal description “disorder”: it concerns the multiplicity of microscopic arrangements compatible with a macroscopic state. (web.mit.edu)

Engineering applications include power generation, refrigeration, and chemical engineering. The Carnot cycle establishes the maximum efficiency of a heat engine operating between two reservoirs:

using absolute temperatures. Real engines operating between those reservoirs have lower efficiencies because of irreversible processes. Equilibrium thermodynamics establishes such limits, while describing rates and evolving temperature or concentration gradients requires additional transport and kinetic theories. (openstax.org)