Функции состояния и линейные интегралы

In a cyclic process, the system returns to its initial state, so state properties like temperature, pressure, and volume return to their original values. However, heat and work exchanged during the cycle can be nonzero. The net heat and net work over the complete cycle need not be zero, even though all state function changes equal zero.

A reversible process keeps the system infinitesimally close to equilibrium, allowing any infinitesimal change to restore both system and surroundings to original states. Work in reversible processes follows dwrev = -pdV. Irreversible processes proceed with finite changes and cannot restore the system and surroundings without external work, occurring when friction or finite compositional, pressure, or temperature changes are present.

An isothermal process maintains constant temperature by placing the system in a thermal bath at fixed temperature, while other properties like volume may change. An adiabatic process involves no heat exchange between system and surroundings, achieved using adiabatic walls, so q and dq equal zero. Both processes can change internal energy and work, but through different mechanisms.

In a constant-volume process, system volume remains fixed using rigid walls, so no pV work occurs. Since work is given by dwrev = -pdV, when dV equals zero, the work term becomes zero regardless of pressure changes. This contrasts with constant-pressure processes, where volume can change and work is performed on or by the system.

In a constant-pressure process, the heat absorbed or released equals the change in enthalpy: ΔH = qp. This relationship makes enthalpy particularly useful for analyzing chemical reactions and physical changes occurring at constant pressure, such as processes in open containers at atmospheric pressure.

Common process types are defined by what remains constant: isothermal processes hold temperature T constant, adiabatic processes maintain zero heat transfer (q = 0), isochoric processes keep volume V constant with zero work, and isobaric processes maintain constant pressure p. Each constraint determines how the system's energy and work are distributed during state changes.

Processes connecting the same initial and final states via different paths are considered different processes. Although state functions like temperature, pressure, and volume depend only on initial and final states, the heat and work exchanged differ for each path. This distinction is central to understanding state functions and exact differentials in thermodynamics.