page_title: Entropy production
section_title: First and second law
hierarchical_section_title: Entropy production / First and second law
caption_attribution_description: English: Modified general thermodynamic system
context_page_description: Entropy production is the amount of entropy which is produced in any irreversible processes such as heat and mass transfer processes including motion of bodies, heat exchange, fluid flow, substances expanding or mixing, anaelastic deformation of solids, and any irreversible thermodynamic cycle, including thermal machines such as power plants, heat engines, refrigerators, heat pumps, and air conditioners.
  In the dual representation entropy-exergy for accounting the second law of thermodynamics it can be expressed in equivalent terms of exergy disruption.
context_section_description: The laws of thermodynamics system apply to well-defined systems. Fig.1 is a general representation of a thermodynamic system. We consider systems which, in general, are inhomogeneous. Heat and mass are transferred across the boundaries (nonadiabatic, open systems), and the boundaries are moving (usually through pistons). In our formulation we assume that heat and mass transfer and volume changes take place only separately at well-defined regions of the system boundary. The expression, given here, are not the most general formulations of the first and second law. E.g. kinetic energy and potential energy terms are missing and exchange of matter by diffusion is excluded.
  The rate of entropy production, denoted by , is a key element of the second law of thermodynamics for open inhomogeneous systems which reads
  Here S is the entropy of the system; Tₖ is the temperature at which the heat flow  enters the system;   represents the entropy flow into the system at position k, due to matter flowing into the system ( are the molar flow and mass flow and Sₘₖ and sₖ are the molar entropy (i.e. entropy per mole) and specific entropy (i.e. entropy per unit mass) of the matter, flowing into the system, respectively);  represents the entropy production rates due to internal processes. The index i in  refers to the fact that the entropy is produced due to irreversible processes. The entropy-production rate of every process in nature is always positive or zero. This is an essential aspect of the second law.
  The ∑'s indicate the algebraic sum of the respective contributions if there are more heat flows, matter flows, and internal processes.
  In order to demonstrate the impact of the second law, and the role of entropy production, it has to be combined with the first law which reads
  with U the internal energy of the system;   the enthalpy flows into the system due to the matter that flows into the system (Hₘₖ its molar enthalpy, hₖ the specific enthalpy (i.e. enthalpy per unit mass)), and dVₖ/dt are the rates of change of the volume of the system due to a moving boundary at position k while pₖ is the pressure behind that boundary; P represents all other forms of power application (such as electrical).
  The first and second law have been formulated in terms of time derivatives of U and S rather than in terms of total differentials dU and dS where it is tacitly assumed that dt > 0. So, the formulation in terms of time derivatives is more elegant. An even bigger advantage of this formulation is, however, that it emphasizes that heat flow and power are the basic thermodynamic properties and that heat and work are derived quantities being the time integrals of the heat flow and the power respectively.
caption: Fig.1 General representation of an inhomogeneous system that consists of a number of subsystems. The interaction of the system with the surroundings is through exchange of heat and other forms of energy, flow of matter, and changes of shape. The internal interactions between the various subsystems are of a similar nature and lead to entropy production.
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